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Journal articles on the topic 'Sawada'

Author: Grafiati

Published: 18 May 2024

Last updated: 26 July 2024

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1

INOUE, SHÛGO, and MUNETOSHI MARUYAMA. "Revision of the genus Plesiochara Sawada (Coleoptera: Staphylinidae: Aleocharinae)." Zootaxa 5165, no. 4 (July 18, 2022): 501–19. http://dx.doi.org/10.11646/zootaxa.5165.4.3.

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The Japanese species of the genus Plesiochara Sawada, 1989 (tribe Aleocharini) are revised. Four species are recognized from Japan: Plesiochara japonica (Sharp, 1874) comb. nov. (removed from Ocalea Erichson), P. nitida Sawada, 1990, P. inflexa sp. nov. and P. rufula sp. nov. Plesiochara fusca Sawada, 1989 is synonymized with P. japonica, syn. nov. All species are described or redescribed, and a key is provided.

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2

Salas, Alvaro H., Cesar A. Gómez S, and Bernardo Acevedo Frias. "Computing Exact Solutions to a Generalized Lax-Sawada-Kotera-Ito Seventh-Order KdV Equation." Mathematical Problems in Engineering 2010 (2010): 1–7. http://dx.doi.org/10.1155/2010/524567.

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The Cole-Hopf transform is used to construct exact solutions to a generalization of both the seventh-order Lax KdV equation (Lax KdV7) and the seventh-order Sawada-Kotera-Ito KdV equation (Sawada-Kotera-Ito KdV7).

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3

Bor, Winny Chepngetich, Owino M. Oduor, and John K. Rotich. "A Lie Symmetry Solutions of Sawada-Kotera Equation." JOURNAL OF ADVANCES IN MATHEMATICS 17 (July 30, 2019): 1–11. http://dx.doi.org/10.24297/jam.v17i0.8364.

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In this article, the Lie Symmetry Analysis is applied in finding the symmetry solutions of the fifth order Sawada-Kotera equation. The technique is among the most powerful approaches currently used to achieveprecise solutions of the partial differential equations that are nonlinear. We systematically show the procedure to obtain the solution which is achieved by developing infinitesimal transformation, prolongations, infinitesimal generatorsand invariant transformations hence symmetry solutions of the fifth order Sawada-Kotera equation. Key Words- Lie symmetry analysis. Sawada-Kotera equation. Symmetry groups. Prolongations. Invariant solutions. Power series solutions. Symmetry solutions.

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4

GUSAROV, VLADIMIR I., and György Makranczy. "Yosiityphlus Sawada, 1971, a new synonym of Thinobius Kiesenwetter, 1844 (Coleoptera: Staphylinidae)." Zootaxa 748, no. 1 (December 1, 2004): 1. http://dx.doi.org/10.11646/zootaxa.748.1.1.

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Based on the analysis of the original description, Yosiityphlus kuroshio Sawada, 1971, initially described as a member of Leptotyphlinae, is transferred to the genus Thinobius Kiesenwetter, 1844, subfamily Oxytelinae. The generic name Yosiityphlus Sawada, 1971 is placed in synonymy with the name Thinobius.

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5

Ahn, Kee-Jeong. "Phylogenetic relationships of the intertidal genus Halorhadinus Sawada and key to the genera of the Liparocephalini (Coleoptera: Staphylinidae: Aleocharinae)." Insect Systematics & Evolution 32, no. 2 (2001): 123–32. http://dx.doi.org/10.1163/187631201x00074.

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AbstractHalorhadinus Sawada is redescribed and illustrations of diagnostic features are presented. Median lobes and parameres of H. aequalis Sawada and H. inaequalis Sawada are described for the first time. A key is provided for separation of the known species of Halorhadinus. Based on contiguous mesocoxal cavities, galea with several setae only on mesal surface and apex with setae, Halorhadinus is hypothesized to be a member of the tribe Liparocephalini. A revised cladistic analysis of the Liparocephalini based on 50 adult characters suggests that Halorhadinus belong to the Liparocephalini with the following patterns of generic relationships (outgroup (Salinamexus Moore & Legner (Halorhadinus Sawada (Amblopusa Casey (Paramblopusa Ahn &Ashe (Diaulota Casey + Liparocephalus Mäklin)))))). Monophyly of the genus Halorhadinus is supported by three synapomorphies (mentum with anterior margin deeply sinuate and antero-lateral parts triangular; ligula round and very long, almost reaching to half of palpi; spatulate setae mostly located on basal part of palpi). A key to the genera of the Liparocephalini is given.

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6

Krishnan, E. V. "On Sawada-Kotera equations." Il Nuovo Cimento B Series 11 92, no. 1 (March 1986): 23–26. http://dx.doi.org/10.1007/bf02729693.

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7

Du, Ya-Hong, Yin-Shan Yun, and Wen-Xiu Ma. "Rational solutions to two Sawada–Kotera-like equations." Modern Physics Letters B 33, no. 09 (March 30, 2019): 1950108. http://dx.doi.org/10.1142/s0217984919501082.

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Two Sawada–Kotera-like equations are introduced by the generalized bilinear operators [Formula: see text] associated with two prime numbers [Formula: see text] and [Formula: see text], respectively. Rational solutions of the two presented Sawada–Kotera-like equations are generated by searching polynomial solutions of the corresponding two generalized bilinear equations.

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8

Li, Li, Meng-Xia Zhang, and Shu-Qiang Lv. "Painlevé Analysis for Supersymmetric Extensions of the Sawada-Kotera Equation." Zeitschrift für Naturforschung A 66, no. 3-4 (April 1, 2011): 165–71. http://dx.doi.org/10.1515/zna-2011-3-405.

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In this paper, Painlevé analysis of supersymmetric extensions of the Sawada-Kotera (SK) equation is performed. It is shown that only two simple supersymmetric extensions of the Sawada-Kotera equation pass the Painlevé test. One of them was proposed by Tian and Liu, the other one is a Bextension of the SK equation.

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9

Kac, Victor, and Johan van de Leur. "Polynomial Tau-Functions of the n-th Sawada–Kotera Hierarchy." Mathematics 12, no. 5 (February 26, 2024): 681. http://dx.doi.org/10.3390/math12050681.

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We give a review of the B-type Kadomtsev–Petviashvili (BKP) hierarchy and find all polynomial tau-functions of the n-th reduced BKP hierarchy (=n-th Sawada–Kotera hierarchy). The name comes from the fact that, for n=3, the simplest equation of the hierarchy is the famous Sawada–Kotera equation.

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10

Tu, Jian-Min, Shou-Fu Tian, Mei-Juan Xu, and Pan-Li Ma. "On quasi-periodic wave solutions and asymptotic behaviors to a (2 + 1)-dimensional generalized variable-coefficient Sawada–Kotera equation." Modern Physics Letters B 29, no. 19 (July 20, 2015): 1550101. http://dx.doi.org/10.1142/s0217984915501018.

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In this paper, a [Formula: see text]-dimensional generalized variable-coefficient Sawada–Kotera (gvcSK) equation is investigated, which describes many nonlinear phenomena in fluid dynamics and plasma physics. Based on the properties of binary Bell polynomials, we present a Hirota’s bilinear equation to the gvcSK equation. By virtue of the Hirota’s bilinear equation, we obtain the N-soliton solutions and the quasi-periodic wave solutions of the gvcSK equation, which can be reduced to the ones of several integrable equations such as Sawada–Kotera, modified Caudrey–Dodd–Gibbon–Sawada–Kotera, isospectral BKP equations and etc. Furthermore, we obtain the relationship between the soliton solutions and periodic solutions by considering the asymptotic properties of the periodic solutions.

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11

Cuccodoro, Giulio, Myoung Hee Kim, and Kee-Jeong Ahn. "Megarthrus of Korea, with description of a new species (Coleoptera: Staphylinidae: Proteininae)." Canadian Entomologist 143, no. 4 (August 2011): 317–31. http://dx.doi.org/10.4039/n11-004.

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AbstractA taxonomic study of Megarthrus Curtis in Korea is presented. The genus is represented in Korea by 10 species including M. coreanus Kim and Cuccodoro sp. nov.Megarthrus corticalis Sharp, M. fennicus Lahtinen, M. incubifer Cuccodoro, M. japonicus Sharp, M. montanus Sawada, M. sawadai Cuccodoro, and M. zerchei Cuccodoro and Löbl are reported from Korea for the first time. A diagnosis of the genus and a key to the Korean species are provided. The new species is diagnosed, described, and illustrated and the other species are diagnosed and illustrated. Species distributions are presented, and the effect of these Korean findings on the level of endemism of the Megarthrus fauna of Japan and Far East Russia is discussed.

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12

GUSAROV, VLADIMIR I. "A revision of Nearctic species of the genera Adota Casey, 1910 and Psammostiba Yosii & Sawada, 1976 (Coleoptera: Staphylinidae: Aleocharinae)." Zootaxa 185, no. 1 (April 24, 2003): 1. http://dx.doi.org/10.11646/zootaxa.185.1.1.

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Holarctic genera Psammostiba Yosii & Sawada, 1976 (new to North America) and Adota Casey, 1910 are redescribed. Halostiba Yosii & Sawada, 1976 is placed in synonymy with Adota Casey, 1910. Keys to Nearctic species of Adota and Psammostiba are provided. Adota colpophila Gusarov, sp. n. from Mexico and Psammostiba kenaii Gusarov, sp. n. from Alaska, British Columbia and California are described. Atheta setositarsis Casey, 1910, At. subintima Casey, 1910, At. scortea Casey, 1911, At. scolopacina Casey, 1911 and At. insons Casey, 1911 are placed in synonymy with Adota maritima (Mannerheim, 1843). Three Palaearctic species, Atheta ushio (Sawada, 1971), At. magnipennis Bernhauer, 1943 and At. madida Bernhauer, 1907 are transferred to Adota. Lectotypes are designated for Atheta massettensis Casey, 1910, At. subintima Casey, 1910, At. scortea Casey, 1911, At. scolopacina Casey, 1911 and At. insons Casey, 1911. Atheta finita Moore & Legner, 1975 (replacement name for At. definita Casey, 1911), At. pavidula Casey, 1911 and At. irrita Casey, 1911 described by Casey in Atheta (Adota) do not belong to Adota. Psammostiba Yosii & Sawada, 1976 is raised to generic rank and Adota comparabilis (Mäklin in Mannerheim, 1853) is transferred to Psammostiba

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13

Wang, Yuhang, and Lianzhong Li. "Lie Symmetry Analysis, Analytical Solution, and Conservation Laws of a Sixth-Order Generalized Time-Fractional Sawada-Kotera Equation." Symmetry 11, no. 12 (November 22, 2019): 1436. http://dx.doi.org/10.3390/sym11121436.

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To discuss the invariance properties of a sixth-order generalized time-fractional Sawada-Kotera equation, on the basis of the Riemann-Liouville derivative, the Lie point symmetry and symmetry reductions are derived. Then the power series theory is used to construct the exact power series solution of the equation. Finally, the conservation laws for a sixth-order generalized time-fractional Sawada-Kotera equation are computed.

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14

Bose, S. K., and D. F. Goble. "Effects of the T-matrix center-of-mass approximation in the Brueckner–Sawada theory of liquid helium II." Canadian Journal of Physics 63, no. 12 (December 1, 1985): 1548–54. http://dx.doi.org/10.1139/p85-257.

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As a model for liquid helium II, we study the Bose–Einstein gas with a two-body interaction potential of the form ~δ(r − a), where r is the interparticle separation. Excitation spectra for various values of a are calculated using the Brueckner–Sawada approach based on the concept of the T matrix. However, unlike the work of Brueckner and Sawada and many other related works that followed, we take into account the dependence of the T matrix on the center-of-mass momentum of the interacting particles. Excitation spectra calculated with and without this dependence, using two different expressions for the two-particle propagator, indicate the validity of the Brueckner and Sawada center-of-mass approximation for physically interesting values of a. The difference between the two spectra is found to increase as a increases.

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15

Qu, Changzheng, Yuqin Si, and Ruochen Liu. "On affine Sawada–Kotera equation." Chaos, Solitons & Fractals 15, no. 1 (January 2003): 131–39. http://dx.doi.org/10.1016/s0960-0779(02)00121-2.

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16

Tian, Kai, and Q. P. Liu. "A supersymmetric Sawada–Kotera equation." Physics Letters A 373, no. 21 (May 2009): 1807–10. http://dx.doi.org/10.1016/j.physleta.2009.03.039.

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17

Gao, Bin-Fang, Q. P. Liu, and Kai Tian. "A super Sawada–Kotera hierarchy." Applied Mathematics Letters 106 (August 2020): 106350. http://dx.doi.org/10.1016/j.aml.2020.106350.

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18

Phélippeau, Marie-Claire. "In memoriam Paul Akio Sawada." Moreana 52 (Number 199-, no. 1-2 (June 2015): 7–9. http://dx.doi.org/10.3366/more.2015.52.1-2.3.

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19

Gallimore, Awen. "Tumor-Associated High Endothelial Venules: Inroads Enabling Immune Control of Cancer Progression." Cancer Immunology Research 10, no. 4 (April 1, 2022): 371. http://dx.doi.org/10.1158/2326-6066.cir-22-0112.

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Abstract Infiltration of lymphocytes into solid tumors represents a significant bottleneck to successful control of tumor growth. The nature of tumor blood vessels is an important factor governing both quantitative and qualitative features of the immune infiltrate. In this issue, Sawada and colleagues identify a genetic signature for blood vessels, most notably high endothelial venules, which are associated with tertiary lymphoid structures and improved clinical outcome. See related article by Sawada et al., p. 468 (4).

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20

Kuramatsu, I. "A. Sawada: Did Luther Venerate Mary?" THEOLOGICAL STUDIES IN JAPAN, no. 41 (2002): 112–19. http://dx.doi.org/10.5873/nihonnoshingaku.2002.112.

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21

Takashige, Masaaki. "Obituary Professor Shozo Sawada (1917-2001)." Ferroelectrics 266, no. 1 (January 2002): 337–39. http://dx.doi.org/10.1080/00150190211325.

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22

Takashige, Masaaki. "Obituary Professor Shozo Sawada (1917-2001)." Ferroelectrics 266, no. 1 (January 2002): 1–3. http://dx.doi.org/10.1080/00150190211455.

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23

LEE, SEUNG-GYU, and KEE-JEONG AHN. "Korean species of the Atheta Thomson subgenus Dimetrota Mulsant & Rey (Coleoptera: Staphylinidae: Aleocharinae) with a description of new species." Zootaxa 5138, no. 4 (May 19, 2022): 401–16. http://dx.doi.org/10.11646/zootaxa.5138.4.3.

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A taxonomic review of the Atheta Thomson subgenus Dimetrota Mulsant & Rey in the Korean Peninsula is presented. The subgenus is represented in Korea by 11 species including a new species, A. (D.) ovata Lee & Ahn, sp. nov. and a new synonym [A. (Badura) tokiokai Sawada = A. (D.) chagangensis Paśnik syn. nov.]. Atheta (D.) yamamotoi Sawada is reported for the first time in the Korean Peninsula and A. (D.) machonryongica in South Korea. A key to Korean species and descriptions with illustrations of habitus photographs and diagnostic characters of three species new to Korea are provided.

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24

Liu, Zeguang. "Abundant mixed lump-kink solutions to a (2+1)-dimensional bSK equation." Modern Physics Letters B 32, no. 26 (September 20, 2018): 1850313. http://dx.doi.org/10.1142/s021798491850313x.

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In this paper, we study lump-kink solutions of a (2+1)-dimensional bidirectional Sawada–Kotera equation and discuss their dynamics. A Hirota bilinear form of a (2+1)-dimensional bidirectional Sawada–Kotera equation is deduced via a dependent logarithmic transformation. Based on this Hirota bilinear equation, we obtain eight classes of lump-kink solutions which combine stripe soliton and lump soliton by using symbolic computations. Our simulation results with the appropriate choice of the arbitrary parameters that show the motion of lump soliton and the process of interaction between lump soliton and a stripe soliton.

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25

Sykes, Catherine, Humayra Dervin, and Rami Sweis. "Editorial: Is there a relationship between dysphagia, chest pain and mucosal innervation in patients with oesophageal motility disorders?" Alimentary Pharmacology & Therapeutics 59, no. 1 (December 12, 2023): 134–35. http://dx.doi.org/10.1111/apt.17808.

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26

SHAVRIN, ALEXEY V. "Microedus LeConte, 1874 (Coleoptera: Staphylindae: Omaliinae: Anthophagini), a new genus for the Palaearctic Region." Zootaxa 5443, no. 2 (April 22, 2024): 205–23. http://dx.doi.org/10.11646/zootaxa.5443.2.4.

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The genus Microedus LeConte, 1874 (Omaliinae: Anthophagini), previously known only from North America, is recorded for the Palaearctic fauna for the first time. Two palaearctic genera were synonymized with Microedus: Altaiodromicus Zerche, 1992 syn. n. and Liophilydrodes Nakane, 1983 syn. n. (replacement name for Lioplax Nakane & K. Sawada, 1956). The genus Microedus was redescribed, illustrated and its taxonomic relations with other genera of the Hygrogeus group are briefly discussed. Four species are (re-)described and illustrated: M. brevitarsis (Champion, 1925) comb. n. (from Geodromicus) (India: Uttarakhand), M. kastcheevi sp. n. (Altai and Dzhungar mts., eastern Kazakhstan), M. schilenkovi (Zerche, 1992) comb. n. (from Altaiodromicus) (Russia (Altai), Kazakhstan), and M. subtilis (Sharp, 1889) comb. n. (from Liophilydrodes) (Russia, Japan). An additional species from Kashmir remains unnamed due the absence of a male, and is compared with the Himalayan M. brevitarsis. A lectotype is designated for Anthophagus subtilis Sharp, 1889. Several new additional combinations are proposed (all these species were previously attributed to the genus Liophilydrodes): M. flavipennis (Watanabe, 1990) comb. n., M. pullus (Nakane & K. Sawada, 1956) comb. n., M. puncticollis (Nakane & K. Sawada, 1956) comb. n., M. suzukii (Watanabe, 1990) comb. n., and M. yamanakai (Watanabe, 1990) comb. n. The following new synonymies are established: M. subtilis = L. subtilis iturupensis Lafer, 2004 syn. n., = L. troglophilus Nakane & K. Sawada, 1956 syn. n. A key to Palaearctic species of Microedus is provided. Mouthparts and the aedeagus of the Nearctic M. austinianus LeConte, 1874 are illustrated for the first time. A distributional map of Microedus from Middle Asia is provided. Microedus schilenkovi is recorded from Kazakhstan for the first time. A checklist of the genus is presented. The genus Microdeus currently contains 16 species, seven in the Nearctic and nine in the Palaearctic Region.

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27

Barrett, T. H. "Confucian Values and Popular Zen: Sekimon Shingaku in Eighteenth-Century Japan. Janine Anderson Sawada." Buddhist Studies Review 11, no. 2 (June 16, 1994): 201–3. http://dx.doi.org/10.1558/bsrv.v11i2.15139.

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28

Ya-Xuan, Yu. "Supersymmetric Sawada–Kotera–Ramani Equation: Bilinear Approach." Communications in Theoretical Physics 49, no. 3 (March 2008): 685–88. http://dx.doi.org/10.1088/0253-6102/49/3/35.

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29

Ma, Hong-Cai, Guo-Ding Ruan, Ke Ni, and Ai-Ping Deng. "Rational solutions to an Caudrey-Dodd-Gibbon-Sawada-Kotera-like equation." Thermal Science 20, no. 3 (2016): 871–74. http://dx.doi.org/10.2298/tsci1603871m.

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30

Goldman, Alberto, Uwe Wollina, Katlein França, Torello Lotti, and Georgi Tchernev. "Lip Repair after Mohs Surgery for Squamous Cell Carcinoma by Bilateral Tissue Expanding Vermillion Myocutaneous Flap (Goldstein Technique Modified by Sawada)." Open Access Macedonian Journal of Medical Sciences 6, no. 1 (January 10, 2018): 93–95. http://dx.doi.org/10.3889/oamjms.2018.034.

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Squamous cell carcinoma is the most common malignancy of the lower lip. Environmental factors such as ultraviolet light exposure, arsenic and smoking are contributing factors to the increasing incidence. Mohs surgery is the treatment of choice ensuring the lowest recurrence rates. The closure of the surgical defects, however, can be a challenge. Multiple and versatile methods of reconstructing vermilion defects have been described. Among these options, Goldstein developed the adjacent ipsilateral vermilion flap based on an arterialized myocutaneous flap. The original technique was modified by Sawada based on bilateral adjacent vermilion advancement flap for closure of central vermilion defects. We report the use of bilateral flaps - Sawada’s technique (instead of unilateral as suggested by Goldstein) in medium (2 cm of extension) to large defects (> 2 cm) to achieve an effective and functional reconstruction of vermillion defects after Mohs surgery for lip cancer.

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31

Li, Wen-Tao, Jia-Heng Li, and Biao Li. "Soliton molecules, asymmetric solitons and some new types of hybrid solutions in (2+1)-dimensional Sawada–Kotera model." Modern Physics Letters B 34, no. 13 (March 4, 2020): 2050141. http://dx.doi.org/10.1142/s0217984920501419.

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Soliton molecules can be formed in both theoretical and experimental situations. In this paper, a new velocity resonance is introduced, which can form soliton molecules for the (2[Formula: see text]+[Formula: see text]1)-dimensional Sawada–Kotera equation. By selecting some suitable parameters for soliton molecules, the asymmetric solitons of the (2[Formula: see text]+[Formula: see text]1)-dimensional Sawada–Kotera equation can be obtained. And, the interactions among multiple soliton molecules are elastic. Furthermore, some new types of hybrid solutions consisting of soliton molecules, lump wave and breather wave can be derived by utilizing velocity resonance, module resonance of wave numbers and long wave limits method. This method of solving the soliton molecules, asymmetric solitons and some new hybrid solutions can also be applied to other nonlinear evolution equations.

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32

徐, 慧琴. "Lump Solution for Sawada-Kotera-Kadovtsev Petviashvili Equation." Advances in Applied Mathematics 09, no. 07 (2020): 1084–91. http://dx.doi.org/10.12677/aam.2020.97128.

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33

Zhou, Jian, Xiang-Gui Li, and Deng-Shan Wang. "The Wronskian Solution and Soliton Resonance of the Nonisospectral Generalised Sawada–Kotera Equation." Zeitschrift für Naturforschung A 70, no. 4 (April 1, 2015): 213–23. http://dx.doi.org/10.1515/zna-2014-0227.

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AbstractThe bilinear form of the nonisospectral generalized Sawada–Kotera equation is derived. With the aid of the Wronskian technique, the Wronskian solution is presented for this equation. The soliton resonance is discussed in inhomogeneous media. Negatons and positons are also obtained.

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34

VALERIE J. MATSUMOTO. "Nikki Sawada Bridges Flynn and What Comes Naturally." Frontiers: A Journal of Women Studies 31, no. 3 (2010): 31. http://dx.doi.org/10.5250/fronjwomestud.31.3.0031.

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35

Inc, Mustafa, Bülent Kılıç, Esra Karataş, and Ali Akgül. "Solitary Wave Solutions for the Sawada-Kotera Equation." Journal of Advanced Physics 6, no. 2 (June 1, 2017): 288–93. http://dx.doi.org/10.1166/jap.2017.1318.

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36

Popowicz, Ziemowit. "Odd Hamiltonian structure for supersymmetric Sawada–Kotera equation." Physics Letters A 373, no. 37 (September 2009): 3315–23. http://dx.doi.org/10.1016/j.physleta.2009.07.057.

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37

Lambert, F., and R. Willox. "Towards an Extension of the Sawada Kotera Hierarchy." Journal of the Physical Society of Japan 59, no. 11 (November 15, 1990): 4188–89. http://dx.doi.org/10.1143/jpsj.59.4188.

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38

Matsumoto, Valerie J. "Nikki Sawada Bridges Flynn and What Comes Naturally." Frontiers: A Journal of Women Studies 31, no. 3 (2010): 31–40. http://dx.doi.org/10.1353/fro.2010.a402742.

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39

LÜ, XING, TAO GENG, CHENG ZHANG, HONG-WU ZHU, XIANG-HUA MENG, and BO TIAN. "MULTI-SOLITON SOLUTIONS AND THEIR INTERACTIONS FOR THE (2+1)-DIMENSIONAL SAWADA-KOTERA MODEL WITH TRUNCATED PAINLEVÉ EXPANSION, HIROTA BILINEAR METHOD AND SYMBOLIC COMPUTATION." International Journal of Modern Physics B 23, no. 25 (October 10, 2009): 5003–15. http://dx.doi.org/10.1142/s0217979209053382.

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In this paper, the (2+1)-dimensional Sawada-Kotera equation is studied by the truncated Painlevé expansion and Hirota bilinear method. Firstly, based on the truncation of the Painlevé series we obtain two distinct transformations which can transform the (2+1)-dimensional Sawada-Kotera equation into two bilinear equations of different forms (which are shown to be equivalent). Then employing Hirota bilinear method, we derive the analytic one-, two- and three-soliton solutions for the bilinear equations via symbolic computation. A formula which denotes the N-soliton solution is given simultaneously. At last, the evolutions and interactions of the multi-soliton solutions are graphically discussed as well. It is worthy to be noted that the truncated Painlevé expansion provides a useful dependent variable transformation which transforms a partial differential equation into its bilinear form and by means of the bilinear form, further study of the original partial differential equation can be conducted.

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40

Shah, Rasool, Fatemah Mofarreh, ElSayed M. Tag, and Nivin A. Ghamry. "Implementation of Analytical Techniques for the Solution of Nonlinear Fractional Order Sawada–Kotera–Ito Equation." Fractal and Fractional 7, no. 4 (March 29, 2023): 299. http://dx.doi.org/10.3390/fractalfract7040299.

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This article uses the Yang transform decomposition method and the homotopy perturbation transform method to study the seventh-order time-fractional Sawada–Kotera–Ito equation. The fractional derivative is taken into account in the Caputo sense. We used the Yang transform with the Adomian decomposition process and homotopy perturbation procedure on the time-fractional Sawada–Kotera–Ito problem to obtain the solution. We looked at a single case and contrasted it with the actual result to validate the methodologies. These techniques create recurrence relations representing the proposed problem’s solution. We then produced graphical representations that allowed us to visually check all of the outcomes in the proposed case for various fractional order values. The results of applying the current methodologies revealed strong connections to the precise resolution of the problem under investigation. The present study also illustrates error analysis. The numerical results obtained using the suggested techniques show that the methods are both simple and have excellent computational merit.

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Riaz, Muhammad Bilal, Faiza Naseer, Muhammad Abbas, Magda Abd El-Rahman, Tahir Nazir, and Choon Kit Chan. "Solitary wave solutions of Sawada-Kotera equation using two efficient analytical methods." AIMS Mathematics 8, no. 12 (2023): 31268–92. http://dx.doi.org/10.3934/math.20231601.

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<abstract><p>The soliton solutions are one of the stable solutions where nonlinearity and dispersion are perfectly balanced. They are used in a wide variety of physical fields, including plasma, solid state, neuronal, biological production, and diffusion processes. Different analytical methods have been used until now to obtain the soliton solutions of the Sawada-Kotera (SK) equation. The purpose of this study is to offer two successful analytical methods for solving the classical (1+1) dimensional Sawada-Kotera (SK) equation. In order to solve the partial differential equation (PDE), both the modified auxiliary equation method (MAEM) and the extended direct algebraic method are applied. The classical fifth-order SK equation is examined in this study, leading to a variety of precise soliton solutions, including single, periodic, and dark soliton, which are obtained analytically. To illustrate the effect of the parameters, the results are shown in graphical form.</p></abstract>

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Khan, M. H. Z., A. S. Jones, and M. T. Haqqani. "Angioleiomyoma of the nasal cavity – report of a case and review of the literature." Journal of Laryngology & Otology 108, no. 3 (March 1994): 244–46. http://dx.doi.org/10.1017/s0022215100126416.

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AbstractAngioleiomyoma of the nasal cavity is an extremely rare tumour (Sawada, 1990). We present an unusual case of angioleiomyoma arising from the lateral wall of the nasal cavity without any symptoms of pain or epistaxis. Another unusual feature was that the tumour clinically resembled an inverted papilloma.

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Hong, Woo-Pyo, and Young-Dae Jung. "Auto-Bäcklund Transformation and Solitary-wave Solutions to Non- integrable Generalized Fifth-order Nonlinear Evolution Equations." Zeitschrift für Naturforschung A 54, no. 8-9 (September 1, 1999): 549–53. http://dx.doi.org/10.1515/zna-1999-8-918.

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We show that the application of the truncated Painlevé expansion and symbolic computation leads to a new class of analytical solitary-wave solutions to the general fifth-order nonlinear evolution equations which include Lax, Sawada-Kotera (SK), Kaup-Kupershmidt (KK), and Ito equations. Some explicit solitary-wave solutions are presented.

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Li, Junjie, Jalil Manafian, Aditya Wardhana, Ali J. Othman, Ismail Husein, Mohaimen Al-Thamir, and Mostafa Abotaleb. "N-Lump to the (2+1)-Dimensional Variable-Coefficient Caudrey–Dodd–Gibbon–Kotera–Sawada Equation." Complexity 2022 (April 29, 2022): 1–32. http://dx.doi.org/10.1155/2022/4383100.

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In this research, the (2 + 1)-dimensional (D) variable-coefficient (VC) Caudrey–Dodd–Gibbon–Kotera–Sawada model used in soliton hypothesis and implemented by operating the Hirota bilinear scheme is studied. A few modern exact analytical outcomes containing interaction between a lump-two kink soliton, interaction between two-lump, the interaction between two-lump soliton, lump-periodic, and lump-three kink outcomes for the (2 + 1)-D VC Caudrey–Dodd–Gibbon–Kotera–Sawada equation by Maple Symbolic packages are obtained. By employing Hirota’s bilinear technique, the extended soliton solutions according to bilinear frame equation are received. For this model, the contemplated model can be got by multi-D binary Bell polynomials (bBPs). In addition, the analytical analysis of the high-order soliton outcomes to present the discipline of outcomes. The effect of the free parameters on the behavior of acquired figures of a few obtained solutions for the nonlinear rational exact cases was also discussed. The above technique could also be employed to get exact solutions for other nonlinear models in physics, applied mathematics, and engineering.

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Yakovleva, Tatiana V., Ilya E. Kutepov, Antonina Yu Karas, Nikolai M. Yakovlev, Vitalii V. Dobriyan, Irina V. Papkova, Maxim V. Zhigalov, et al. "EEG Analysis in Structural Focal Epilepsy Using the Methods of Nonlinear Dynamics (Lyapunov Exponents, Lempel–Ziv Complexity, and Multiscale Entropy)." Scientific World Journal 2020 (February 11, 2020): 1–13. http://dx.doi.org/10.1155/2020/8407872.

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This paper analyzes a case with the patient having focal structural epilepsy by processing electroencephalogram (EEG) fragments containing the “sharp wave” pattern of brain activity. EEG signals were recorded using 21 channels. Based on the fact that EEG signals are time series, an approach has been developed for their analysis using nonlinear dynamics tools: calculating the Lyapunov exponent’s spectrum, multiscale entropy, and Lempel–Ziv complexity. The calculation of the first Lyapunov exponent is carried out by three methods: Wolf, Rosenstein, and Sano–Sawada, to obtain reliable results. The seven Lyapunov exponent spectra are calculated by the Sano–Sawada method. For the observed patient, studies showed that with medical treatment, his condition did not improve, and as a result, it was recommended to switch from conservative treatment to surgical. The obtained results of the patient’s EEG study using the indicated nonlinear dynamics methods are in good agreement with the medical report and MRI data. The approach developed for the analysis of EEG signals by nonlinear dynamics methods can be applied for early detection of structural changes.

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GHANY, HOSSAM A., and ABD-ALLAH HYDER. "EXACT SOLUTIONS FOR WICK-TYPE STOCHASTIC SAWADA-KOTERA EQUATION." Poincare Journal of Analysis and Applications 01, no. 01 (June 27, 2014): 39–46. http://dx.doi.org/10.46753/pjaa.2014.v01i01.005.

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Hu, Xing-Biao, Zuo-Nong Zhu, and Dao-Liu Wang. "A Differential-Difference Caudrey-Dodd-Gibbon-Kotera-Sawada Equation." Journal of the Physical Society of Japan 69, no. 4 (April 15, 2000): 1042–49. http://dx.doi.org/10.1143/jpsj.69.1042.

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Zuo, Da-Wei, Hui-Xia Mo, and Hui-Ping Zhou. "Multi-Soliton Solutions of the Generalized Sawada–Kotera Equation." Zeitschrift für Naturforschung A 71, no. 4 (April 1, 2016): 305–9. http://dx.doi.org/10.1515/zna-2015-0445.

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AbstractKorteweg–de Vries (KdV)-type equations can describe the nonlinear phenomena in shallow water waves, stratified internal waves, and ion-acoustic waves in plasmas. In this article, the two-dimensional generalization of the Sawada–Kotera equation, one of the KdV-type equations, is discussed by virtue of the Bell polynomials and Hirota method. The results show that there exist multi-soliton solutions for such an equation. Relations between the direction of the soliton propagation and coordinate axes are shown. Elastic interaction with the multi-soliton solutions are analysed.

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Mao, Hui, Q. P. Liu, and Lingling Xue. "Supersymmetric Sawada-Kotera Equation: Bäcklund-Darboux Transformations and Applications." Journal of Nonlinear Mathematical Physics 25, no. 3 (July 3, 2018): 375–86. http://dx.doi.org/10.1080/14029251.2018.1494779.

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Wu, Lihua, Guoliang He, and Xianguo Geng. "Algebro-geometric solutions to the modified Sawada-Kotera hierarchy." Journal of Mathematical Physics 53, no. 12 (December 2012): 123513. http://dx.doi.org/10.1063/1.4764886.

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