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Journal articles on the topic 'Singular Schrodinger equation'

Author: Grafiati

Published: 10 March 2023

Last updated: 31 July 2025

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1

Danladi, Ali, Alhaji Tahir, and Hadi Rezazadeh. "Modulation Instability, Dark and Singular Soliton for Weakly Nonlocal Schrodinger Equation." European Journal of Mathematical Analysis 5 (May 23, 2025): 14. https://doi.org/10.28924/ada/ma.5.14.

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The optical soliton solution of nonlinear complex models holds significant importance in nonlinear optics and communication systems. Considering nonlinear complex models, often described by equations like the nonlinear Schrodinger equation (NLSE), plays a crucial role in defining the balance between dispersive and nonlinear effects, enabling the formation and maintenance of solitons over long distances. This stability is crucial for signal integrity in optical communication systems. The investigation of optical soliton solutions from nonlinear complex models is sometimes complicated. With this

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2

Troy, W. C. "New singular standing wave solutions of the nonlinear Schrodinger equation." Journal of Differential Equations 267, no. 2 (2019): 979–1000. http://dx.doi.org/10.1016/j.jde.2019.01.031.

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3

Zhunussova, Zh Kh. "The surface to singular solitonic solution of the nonlinear Schrodinger equation." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 88, no. 4 (2017): 26–33. http://dx.doi.org/10.31489/2017m4/26-33.

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4

Tekercioglu, Ramazan. "On the traveling wave solutions of pulse propagation in monomode fiber via the extended Kudryashov’s approach." Thermal Science 26, Spec. issue 1 (2022): 49–59. http://dx.doi.org/10.2298/tsci22s1049t.

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In this research paper, we tackle with the solitary wave solutions to the pulse prop?agation in monomode optic fiber by defining non-linear Schrodinger equation with higher order. We applied the extended Kudryashov?s method with Bernoulli-Riccati equation and successfully gained soliton solutions and their contour, 2-D and 3-D graphical representations, such as dark, singular, periodic and kink type solutions. We also discussed the obtained results in the related section.

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5

Lin, Yuanhua, and Liping He. "Existence of Traveling Wave Fronts for a Generalized Nonlinear Schrodinger Equation." Advances in Mathematical Physics 2022 (August 16, 2022): 1–6. http://dx.doi.org/10.1155/2022/9638150.

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In the presented paper, a generalized nonlinear Schr o dinger equation without delay convolution kernel and with special delay convolution kernel is investigated. By using the geometric singular perturbation theory, the existence of traveling wave fronts is proved. Firstly, we show that such traveling wave fronts exist without delay by non-Hamiltonian qualitative analysis. Then, for the generalized nonlinear Schr o dinger equation with a special local strong delay convolution kernel, the desired heteroclinic orbit is obtained by using the Fredholm theory.

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6

Vshivteev, A. S., N. V. Norin, and V. N. Sorokin. "Spectral problem for the Schrodinger equation with singular potential polynomial of even degree." Russian Physics Journal 39, no. 5 (1996): 442–56. http://dx.doi.org/10.1007/bf02436783.

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7

Kapitula, Todd. "Bifurcating bright and dark solitary waves for the perturbed cubic-quintic nonlinear Schrödinger equation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 128, no. 3 (1998): 585–629. http://dx.doi.org/10.1017/s030821050002165x.

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The existence of bright and dark multi-bump solitary waves for Ginzburg–Landau type perturbations of the cubic-quintic Schrodinger equation is considered. The waves in question are not perturbations of known analytic solitary waves, but instead arise as a bifurcation from a heteroclinic cycle in a three-dimensional ODE phase space. Using geometric singular perturbation techniques, regions in parameter space for which 1-bump bright and dark solitary waves will bifurcate are identified. The existence of N-bump dark solitary waves (N ≧ 1) is shown via an application of the Exchange Lemma with Exp

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8

ESTEVEZ, P. G., and G. A. HERNAEZ. "Painleve Analysis and Singular Manifold Method for a (2 + 1) Dimensional Non-Linear Schrodinger Equation." Journal of Non-linear Mathematical Physics 8, Supplement (2001): 106. http://dx.doi.org/10.2991/jnmp.2001.8.supplement.19.

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9

Raza, Nauman, Riaz ur Rahman, Aly Seadawy, and Adil Jhangeer. "Computational and bright soliton solutions and sensitivity behavior of Camassa–Holm and nonlinear Schrödinger dynamical equation." International Journal of Modern Physics B 35, no. 11 (2021): 2150157. http://dx.doi.org/10.1142/s0217979221501575.

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In this paper, we sketch and scrutinize the solitonic wave solution of Camassa–Holm equation by applying Kudryashov’s new method. We promote the algorithm of our new method to find the new solutions of this essential model. Camassa–Holm equation is a recent model in the point of distortion of hierarchies composition of integrability systems. It has been displayed that these solutions have the shape of dark, bright and singular solitons solutions of Camassa–Holm nonlinear Schrodinger equation. Graphically changing of extracted results of this model (CH) has been separated to grasp the substanti

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10

Shalaby, A. M. "Dimensional Regularization of the Spatial wave function for a singular contact interaction in the Relativistic Schrodinger Equation." Journal of Physics: Conference Series 670 (January 25, 2016): 012045. http://dx.doi.org/10.1088/1742-6596/670/1/012045.

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11

Bai, Ruobing, and Tarek Saanouni. "Non global solutions for non-radial inhomogeneous nonlinear Schrodinger equations." Electronic Journal of Differential Equations 2025, no. 01-?? (2025): 55. https://doi.org/10.58997/ejde.2025.55.

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This work concerns the inhomogeneous Schr\"odinger equation $$ \mathrm{i}\partial_t u-\mathcal{K}_{s,\lambda}u +F(x,u)=0 , \quad u(t,x):\mathbb{R}\times\mathbb{R}^N\to\mathbb{C}. $$ Here, \(s\in\{1,2\}\), \(N>2s\) and \(\lambda>-(N-2)^2/4\). The linear Schr\"odinger operator is \(\mathcal{K}_{s,\lambda}:= (-\Delta)^s +(2-s)\frac{\lambda}{|x|^2}\), and the focusing source term can be local or non-local $$ F(x,u)\in\{|x|^{-2\tau}|u|^{2(q-1)}u,|x|^{-\tau}|u|^{p-2} \big(J_\alpha *|\cdot|^{-\tau}|u|^p\big)u\}. $$ The Riesz potential is \(J_\alpha(x)=C_{N,\alpha}|x|^{-(N-\alpha)}\), for certai

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12

CASAHORRÁN, J. "A NEW SUPERSYMMETRIC VERSION OF THE ABRAHAM-MOSES METHOD FOR SYMMETRIC POTENTIALS." Reviews in Mathematical Physics 08, no. 05 (1996): 655–68. http://dx.doi.org/10.1142/s0129055x96000226.

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Starting from the one-dimensional Schrodinger equation with symmetric potential Vs(x), a general method is presented in order to obtain a family of partially isospectral hamiltonians. Arguments concerning supersymmetric transformations, factorization procedures and Riccati equations are invoked along the article. As a result of the appearance of singular superpotentials, the physical meaning of our method can be summarized as follows: only the odd wave-functions of the original potential Vs(x) are transported via supersymmetry into the Hilbert space associated with the partner Vp(x). In such a

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13

ALHEJAILI, WEAAM, ABDUL-MAJID WAZWAZ, SARAH ALOMAIR, and S. A. EL-TANTAWY. "Families of soliton solutions and other exact solutions of the (2+1)-dimensional chiral nonlinear Schrödinger equation." Romanian Reports in Physics 76, no. 2 (2025): 104. https://doi.org/10.59277/romrepphys.2025.77.104.

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In this work, we study the (2+1)-dimensional chiral nonlinear Schrodinger equation (CNLSE), which is essential in the fields of nonlinear optics, plasma physics, and fluid mechanics. Traveling wave analytical algorithms reveal a variety of solitons and other exact solutions with distinct physical structures. To obtain the families of exact solutions we implement effective methods, including hyperbolic schemes, trigonometric techniques, singular and periodic waveforms, and rational functions methods. Utilizing various forms of the proposed techniques we uncover a wealth of traveling wave soluti

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14

Sarafanov, G. F., and A. A. Utkin. "MODEL OF FORMATION AND PROPAGATION OF SLIP BANDS IN METALS." Problems of Strength and Plasticity 85, no. 1 (2023): 5–13. http://dx.doi.org/10.32326/1814-9146-2023-85-1-5-13.

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A theoretical study of the processes of localization of plastic deformation in metals has been carried out. Within the framework of the system of evolutionary equations for dislocation density, taking into account the multiplication and annihilation of dislocations, the possibility of a running solution for the slip strip is established. It is shown that the initial system has two equilibrium states. For the total dislocation density and dislocation charge normalized to a stationary homogeneous solution for dislocation density, these are the states (0,0) and (1,0) on the phase plane of the abo

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15

Wang, Ming-Yue, Anjan Biswas, Yakup Yıldırım, Luminita Moraru, Simona Moldovanu, and Hashim M. Alshehri. "Optical Solitons for a Concatenation Model by Trial Equation Approach." Electronics 12, no. 1 (2022): 19. http://dx.doi.org/10.3390/electronics12010019.

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This paper addresses the newly proposed concatenation model by the usage of trial equation approach. The concatenation is a chain model that is a combination of the nonlinear Schrodinger’s equation, Lakshmanan–Porsezian–Daniel model as well as the Sasa–Satsuma equation. The recovered solutions are displayed in terms of dark solitons, singular solitons, cnoidal waves and singular periodic waves. The trial equation approach enables to recover a wide spectrum of solutions to the governing model. The numerical schemes give a visual perspective to the solutions derived analytically.

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16

C., Moameni Abbas and Offin Daniel. "Positive Solutions for Singular Quasilinear Schrodinger Equations with One Parameter, II." Journal of Partial Differential Equations 23, no. 3 (2010): 222–34. http://dx.doi.org/10.4208/jpde.v23.n3.2.

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17

Javid, Ahmad, and Nauman Raza. "Chiral solitons of the (1 + 2)-dimensional nonlinear Schrodinger’s equation." Modern Physics Letters B 33, no. 32 (2019): 1950401. http://dx.doi.org/10.1142/s0217984919504013.

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In this work, dark and singular soliton solutions of the (1[Formula: see text]+[Formula: see text]2)-dimensional chiral nonlinear Schrödinger’s equation are obtained and analyzed dynamically along with graphical depictions. The extraction of these chiral solitons is carried out using two integration tools such as the modified simple equation method and the [Formula: see text]-expansion method. The validity conditions for the existence of these solitons are also retrieved. It is highlighted that the solitons retrieved here are of chiral nature.

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18

Deng, Jin, Aliang Xia, and Jianfu Yang. "Positive vortex solutions and phase separation for coupled Schrodinger system with singular potential." Electronic Journal of Differential Equations 2020, no. 01-132 (2020): 108. http://dx.doi.org/10.58997/ejde.2020.108.

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We consider the existence of rotating solitary waves (vortices) for a coupled Schrodinger equations by finding solutions to the singular system $$\displaylines{ -\Delta u+\lambda_1 u+\frac{u}{|x|^2}=\mu_1 u^3+\beta u v^2, \quad x\in\mathbb{R}^2, \cr -\Delta v+\lambda_2 v+\frac{v}{|x|^2}=\mu_2 v^3+\beta u^2 v, \quad x\in\mathbb{R}^2, \cr u,v \geq 0,\quad x\in\mathbb{R}^2, }$$ where \(\lambda_1,\lambda_2,\mu_1, \mu_2\) are positive parameters, \(\beta\neq 0\). We show that this system has a positive least energy solution for the cases When either \(\beta\) is negative or \(\beta\) is positive an

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19

Raza, Nauman, and Ahmad Javid. "Optical dark and dark-singular soliton solutions of (1+2)-dimensional chiral nonlinear Schrodinger’s equation." Waves in Random and Complex Media 29, no. 3 (2018): 496–508. http://dx.doi.org/10.1080/17455030.2018.1451009.

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20

Eliseev, Alexander Georgievich, and Pavel Vladimirovich Kirichenko. "Regularized asymptotics of the solution of a singularly perturbedmixed problem on the semiaxis for an equation of Schrodinger type in the presence of a strong turning point for the limit operator." Chebyshevskii Sbornik 24, no. 1 (2023): 50–68. http://dx.doi.org/10.22405/2226-8383-2023-24-1-50-68.

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21

Badiale, Marino, Vieri Benci, and Sergio Rolando. "A nonlinear elliptic equation with singular potential and applications to nonlinear field equations." December 23, 2009. https://doi.org/10.4171/jems/83.

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We study existence and asymptotic properties of solutions to a semilinear elliptic equation in the whole space. The equation has a cylindrical symmetry and we find cylindrical solutions. The main features of the problem are that the potential has a large set of singularities (i.e. a subspace), and that the nonlinearity has a double power-like behaviour, subcritical at infinity and supercritical near the origin. We also show that our results imply the existence of solitary waves with nonvanishing angular momentum for nonlinear evolution equations of Schrodinger and Klein-Gordon type.

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22

Gu, Yongyi, Jalil Manafian, Mustafa Z. Mahmoud, Sukaina Tuama Ghafel, and Onur Alp Ilhan. "New soliton waves and modulation instability analysis for a metamaterials model via the integration schemes." International Journal of Nonlinear Sciences and Numerical Simulation, October 13, 2022. http://dx.doi.org/10.1515/ijnsns-2021-0443.

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Abstract In this paper, the exact analytical solutions to the generalized Schrödinger equation are investigated. The Schrodinger type equations bearing nonlinearity are the important models that flourished with the wide-ranging arena concerning plasma physics, nonlinear optics, fluid-flow, and the theory of deep-water waves, etc. In this exploration, the soliton and other traveling wave solutions in an appropriate form to the generalized nonlinear Schrodinger equation by means of the extended sinh-Gordon equation expansion method, tan(Γ(ϖ))-expansion method, and the improved cos(Γ(ϖ)) function

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23

Ghosh, Santu, Biswajit Das, Netai Das, and Arijit Ghoshal. "Calculation of the critical bound-continuum limit of the one-electron atoms interacting with the generalised exponential cosine screened potential using scattering formalism." Journal of Physics A: Mathematical and Theoretical, February 21, 2025. https://doi.org/10.1088/1751-8121/adb91e.

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Abstract The critical values of the screening parameters (β and θ) of the generalised exponential cosine screened potential (GECSCP), characterising the critical bound-continuum limit of the one-electron atoms interacting with this potential, have been calculated accurately by exploring the scattering state solution of the corresponding Schrodinger equation at the zero-energy. It is shown that the scattering length (SL) corresponding to an attractive potential becomes singular and the zero-energy resonance occurs when the potential loses the ability of supporting any bound state. More generall

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24

Rehman, S. U., Aly R. Seadawy, M. Younis, S. T. R. Rizvi, T. A. Sulaiman, and A. Yusuf. "Modulation instability analysis and optical solitons of the generalized model for description of propagation pulses in optical fiber with four non-linear terms." Modern Physics Letters B, December 24, 2020, 2150112. http://dx.doi.org/10.1142/s0217984921501128.

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In this article, we investigate the optical soiltons and other solutions to Kudryashov’s equation (KE) that describe the propagation of pulses in optical fibers with four non-linear terms. Non-linear Schrodinger equation with a non-linearity depending on an arbitrary power is the base of this equation. Different kinds of solutions like optical dark, bright, singular soliton solutions, hyperbolic, rational, trigonometric function, as well as Jacobi elliptic function (JEF) solutions are obtained. The strategy that is used to extract the dynamics of soliton is known as [Formula: see text]-model e

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25

Khuri, Suheil, and Abdul-Majid Wazwaz. "Bright and dark optical solitons in optical metamaterials using a variety of distinct schemes for a generalized Schrodinger equation." International Journal of Numerical Methods for Heat & Fluid Flow, September 11, 2024. http://dx.doi.org/10.1108/hff-05-2024-0408.

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Purpose The purpose of this study is to investigate the nonlinear Schrödinger equation (NLS) incorporating spatiotemporal dispersion and other dispersive effects. The goal is to derive various soliton solutions, including bright, dark, singular, periodic and exponential solitons, to enhance the understanding of soliton propagation dynamics in nonlinear metamaterials (MMs) and contribute new findings to the field of nonlinear optics. Design/methodology/approach The research uses a range of powerful mathematical approaches to solve the NLS. The proposed methodologies are applied systematically t

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26

Muhammad, Jan, Qasim Ali, and Usman Younas. "Three component coupled fractional nonlinear Schrodinger equations: Diversity of exact optical solitonic structures." Modern Physics Letters B 38, no. 36 (2024). https://doi.org/10.1142/s0217984924503731.

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Multicomponent-coupled nonlinear Schrodinger-type equations are significant mathematical models that have their origins in numerous disciplines such as the nonlinear optics, theory of deep water waves, plasma physics, and fluid dynamics, and many others. This work is mainly concerned to the study of fractional optical soliton solutions of the truncated fractional three component coupled nonlinear Schrödinger-type system. The study of soliton theory plays a crucial role in the telecommunication industry by the utilization of nonlinear optics. The principal area of research in the field of optic

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27

Біргебаев, А. Б. "ГЛАДКОСТЬ РЕШЕНИЙ (РАЗДЕЛИМОСТЬ) НЕЛИНЕЙНОГО СТАЦИОНАРНОГО УРАВНЕНИЯ ШРЕДИНГЕРА". BULLETIN Series Physical and Mathematical Sciences 80, № 4(2022) (2023). http://dx.doi.org/10.51889/8935.2022.97.74.002.

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Микробөлшектердің әртүрлі күш өрістеріндегі қозғалыс теңдеуі Шредингер толқынының теңдеуі болып табылады. Кванттық механиканың көптеген сұрақтары, атап айтқанда электромагниттік толқындардың жылулық сәулеленуі сингулярлы дифференциалдық операторлардың бөліну мәселесіне әкеледі. Осындай операторлардың бірі жоғарыдағы Шредингер операторы болып табылады. Бұл жұмыста аталған оператор функционалдық талдау әдістерімен зерттеледі. Шешімнің болуы және Гильберт кеңістігіндегі оператордың бөліктенуі үшін жеткілікті шарттар табылды. Барлық теоремалар бастапқыда Штурм-Лиувилл теңдеуінің үлгісі үшін дәлелд

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28

Ambrosio, Vincenzo. "On a singularly perturbed fractional relativistic Schrodinger-Choquard equation." Communications in Contemporary Mathematics, December 28, 2023. http://dx.doi.org/10.1142/s021919972350061x.

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29

Akter, Shahrina, Md Golam Hafez, and Rathinasamy Sakthivel. "Propagation of collisional among multi-soliton, multi-singular solition androgue wave around the critical values in an unmagetized plasma." Physica Scripta, February 19, 2024. http://dx.doi.org/10.1088/1402-4896/ad2ad3.

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Abstract Progress in understanding the propagation characteristics of (i) collisional acoustic among multisoliton and multi-singular soliton around the critical values and their corresponding phase shifts and&#xD;(ii) collision between two rogue waves (RWs) propagating toward each in a plasma environment is&#xD;presented. The considered plasma environment consists of mobile cold positrons, immobile positive&#xD;ions and (r,q)-distributed hot positrons, and electrons. To accomplish our goal, the coupled modified&#xD;Korteweg-de Vries equations (mKdVEs) and nonlinear Schrodinger

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