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Journal articles on the topic 'Sinh-Gordon model'

Author: Grafiati

Published: 2 November 2024

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1

Sulaiman, Tukur Abdulkadir, and Hasan Bulut. "The new extended rational SGEEM for construction of optical solitons to the (2+1)–dimensional Kundu–Mukherjee–Naskar model." Applied Mathematics and Nonlinear Sciences 4, no. 2 (December 24, 2019): 513–22. http://dx.doi.org/10.2478/amns.2019.2.00048.

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AbstractThis work proposes the new extended rational sinh-Gordon equation expansion technique (SGEEM). The computational approach is formulated based on the well-known sinh-Gordon equation. The proposed technique generalizes the sine-Gordon/sinh-Gordon expansion methods in a rational format. The efficiency of the suggested technique is tested on the (2+1)imensional Kunduukherjeeaskar (KMN) model. Various of optical soliton solutions have been obtained using this new method. The conditions which guarantee the existence of valid solitons are given.

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2

Alzaleq, Lewa’, Du’a Al-zaleq, and Suboh Alkhushayni. "Traveling Waves for the Generalized Sinh-Gordon Equation with Variable Coefficients." Mathematics 10, no. 5 (March 4, 2022): 822. http://dx.doi.org/10.3390/math10050822.

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The sinh-Gordon equation is simply the classical wave equation with a nonlinear sinh source term. It arises in diverse scientific applications including differential geometry theory, integrable quantum field theory, fluid dynamics, kink dynamics, and statistical mechanics. It can be used to describe generic properties of string dynamics for strings and multi-strings in constant curvature space. In the present paper, we study a generalized sinh-Gordon equation with variable coefficients with the goal of obtaining analytical traveling wave solutions. Our results show that the traveling waves of the variable coefficient sinh-Gordon equation can be derived from the known solutions of the standard sinh-Gordon equation under a specific selection of a choice of the variable coefficients. These solutions include some real single and multi-solitons, periodic waves, breaking kink waves, singular waves, periodic singular waves, and compactons. These solutions might be valuable when scientists model some real-life phenomena using the sinh-Gordon equation where the balance between dispersion and nonlinearity is perturbed.

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3

FENG, SZE-SHIANG, and GUANG-JIONG NI. "GAUSSIAN EFFECTIVE POTENTIAL ANALYSIS OF SINH(SINE)–GORDON MODELS NEW REGULARIZATION–RENORMALIZATION SCHEME." International Journal of Modern Physics A 14, no. 27 (October 30, 1999): 4259–74. http://dx.doi.org/10.1142/s0217751x99002001.

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Using the new regularization and renormalization scheme recently proposed by Yang and used by Ni et al., we analyze the sine–Gordon and sinh–Gordon models within the framework of Gaussian effective potential in D+1 dimensions. Our analysis suffers no divergence and so does not suffer from the manipulational obscurities in the conventional analysis of divergent integrals. Our main conclusions agree exactly with those of Ingermanson for D=1,2 but disagree for D=3: the D=3 sinh(sine)–Gordon model is nontrivial. Furthermore, our analysis shows that for D=1,2, the running coupling constant (RCC) has poles for sine–Gordon model (γ2<0) and the sinh–Gordon model (γ2>0) has a possible critical point [Formula: see text] while for D=3, the RCC has poles for both γ2>0 and γ2<0.

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4

BABUJIAN, H., and M. KAROWSKI. "TOWARDS THE CONSTRUCTION OF WIGHTMAN FUNCTIONS OF INTEGRABLE QUANTUM FIELD THEORIES." International Journal of Modern Physics A 19, supp02 (May 2004): 34–49. http://dx.doi.org/10.1142/s0217751x04020294.

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The purpose of the "bootstrap program" for integrable quantum field theories in 1+1 dimensions is to construct a model in terms of its Wightman functions explicitly. In this article, the program is mainly illustrated in terms of the sine-Gordon and the sinh-Gordon model and (as an exercise) the scaling Ising model. We review some previous results on sine-Gordon breather form factors and quantum operator equations. The problem to sum over intermediate states is attacked in the short distance limit of the two point Wightman function for the sinh-Gordon and the scaling Ising model.

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5

PILLIN, MATHIAS. "THE FORM FACTORS IN THE SINH–GORDON MODEL." International Journal of Modern Physics A 13, no. 26 (October 20, 1998): 4469–86. http://dx.doi.org/10.1142/s0217751x98002158.

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The most general solution to the form factor problem in the sinh–Gordon model is presented in an explicit way. The linearly independent classes of solutions correspond to powers of the elementary field. We show how the form factors of exponential operators can be obtained from the general solution by adjusting free parameters. The general formula obtained in the sinh–Gordon case reproduces the form factors of the scaling Lee–Yang model in a certain limit of the coupling constant.

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6

Corrigan, E., and G. W. Delius. "Boundary breathers in the sinh-Gordon model." Journal of Physics A: Mathematical and General 32, no. 49 (November 30, 1999): 8601–14. http://dx.doi.org/10.1088/0305-4470/32/49/303.

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7

Sklyanin, E. K. "Exact quantization of the sinh-Gordon model." Nuclear Physics B 326, no. 3 (November 1989): 719–36. http://dx.doi.org/10.1016/0550-3213(89)90552-x.

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8

Volkov, A. Yu. "Liouville's equation and the lattice sinh-Gordon model." Journal of Soviet Mathematics 46, no. 5 (September 1989): 2065–77. http://dx.doi.org/10.1007/bf01096089.

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9

GRIGORIEV, MAXIM, and ARKADY TSEYTLIN. "REDUCED MODEL FOR SUPERSTRINGS ON AdSn × Sn." International Journal of Modern Physics A 23, no. 14n15 (June 20, 2008): 2107–17. http://dx.doi.org/10.1142/s0217751x08040652.

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We review the Pohlmeyer reduction of the superstring sigma model on AdSn × Sn leading to a gauged WZW model with an integrable potential. In particular, we consider the case of GS superstrings on AdS3 × S3 supported by RR flux. The bosonic part of the reduced Lagrangian is given by the sum of the complex sine-Gordon Lagrangian and its sinh-Gordon counterpart. We determine the corresponding fermionic part and discuss possible 2d supersymmetry of the reduced action.

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10

Spano, N. I., A. R. Aguirre, J. F. Gomes, and A. H. Zimerman. "Fusing defect for theN= 2 super sinh-Gordon model." Journal of Physics: Conference Series 670 (January 25, 2016): 012049. http://dx.doi.org/10.1088/1742-6596/670/1/012049.

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11

Babelon, O., and L. Bonora. "Sinh-Gordon model as a spontaneously broken conformal theory." Physics Letters B 267, no. 1 (September 1991): 71–80. http://dx.doi.org/10.1016/0370-2693(91)90526-v.

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12

Koubek, A., and G. Mussardo. "On the operator content of the sinh-Gordon model." Physics Letters B 311, no. 1-4 (July 1993): 193–201. http://dx.doi.org/10.1016/0370-2693(93)90554-u.

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13

Sulaiman, Tukur Abdulkadir, Hasan Bulut, and Haci Mehmet Baskonus. "Construction of various soliton solutions via the simplified extended sinh-Gordon equation expansion method." ITM Web of Conferences 22 (2018): 01062. http://dx.doi.org/10.1051/itmconf/20182201062.

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In this paper, we present the simplified version of the extended sinh-Gordon equation expansion method. The newly proposed approach is based on the well-known sinh-Gordon equation and a travelling wave transformation. We successfully employed this approach to the (2+1)-dimensional nonlinear Chiral Schrodinger's and various solitary wave solutions to the studied nonlinear model are successfully constructed. The (2+1)-dimensional nonlinear Chiral Schrodinger's equation describes the edge states of the fractional quantum hall effect. The 2D and 3D surfaces of some of the obtained solutions are plotted.

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14

Bajnok, Zoltan, and Fedor Smirnov. "Diagonal finite volume matrix elements in the sinh-Gordon model." Nuclear Physics B 945 (August 2019): 114664. http://dx.doi.org/10.1016/j.nuclphysb.2019.114664.

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15

Ahn, Changrim, and Rafael I. Nepomechie. "Exact solution of the supersymmetric sinh-Gordon model with boundary." Nuclear Physics B 586, no. 3 (October 2000): 611–40. http://dx.doi.org/10.1016/s0550-3213(00)00440-5.

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16

Vaidya, Sachindeo. "The quantum sinh-Gordon model in noncommutative (1+1) dimensions." Physics Letters B 655, no. 5-6 (November 2007): 294–97. http://dx.doi.org/10.1016/j.physletb.2007.08.089.

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17

CORRIGAN, E. "ON DUALITY AND REFLECTION FACTORS FOR THE SINH–GORDON MODEL WITH A BOUNDARY." International Journal of Modern Physics A 13, no. 16 (June 30, 1998): 2709–22. http://dx.doi.org/10.1142/s0217751x98001372.

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The sinh–Gordon model with integrable boundary conditions is considered in low order perturbation theory. It is pointed out that results obtained by Ghoshal for the sine–Gordon breather reflection factors suggest an interesting dual relationship between models with different boundary conditions. Ghoshal's formula for the lightest breather is checked perturbatively to O(β2) in the special set of cases in which the ϕ→-ϕ symmetry is maintained. It is noted that the parametrization of the boundary potential which is natural for the semiclassical approximation also provides a good parametrizaiton at the "free-fermion" point.

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18

Negro, Stefano. "On sinh–Gordon thermodynamic Bethe ansatz and fermionic basis." International Journal of Modern Physics A 29, no. 20 (August 6, 2014): 1450111. http://dx.doi.org/10.1142/s0217751x14501115.

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We review the construction of the fermionic basis for sinh–Gordon model and investigate numerically the ultraviolet limit of the one-point functions. We then compare the predictions obtained from this formalism against previously established results.

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19

ABLIKIM, M., and E. CORRIGAN. "ON THE PERTURBATIVE EXPANSION OF BOUNDARY REFLECTION FACTORS OF THE SUPERSYMMETRIC SINH–GORDON MODEL." International Journal of Modern Physics A 16, no. 04 (February 10, 2001): 625–40. http://dx.doi.org/10.1142/s0217751x01002944.

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The supersymmetric sinh–Gordon model on a half-line with integrable boundary conditions is considered perturbatively to verify conjectured exact reflection factors to one loop order. Propagators for the boson and fermion fields restricted to a half-line contain several novel features and are developed as prerequisites for the calculations.

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20

POPOV, A. D. "SOLUTIONS TO YANG–MILLS EQUATIONS: QUASI-INSTANTONS, QUASI-MONOPOLES AND QUASI-VORTICES." International Journal of Modern Physics A 07, no. 02 (January 20, 1992): 269–85. http://dx.doi.org/10.1142/s0217751x9200017x.

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Yang–Mills equations for semisimple gauge Lie groups G in d = 4 spaces with signatures (+ + + +) and (+ + − −) are considered. Generalizations of the one-monopole and one-instanton solutions to these equations for the group [Formula: see text] and for its real forms are obtained. For gauge fields of the vortex type, the Ansätze permitting the reduction of d = 4 self-duality equations to the d = 2 Liouville, sinh–Gordon and sine–Gordon, G/H sigma-model equations and to the equations of the relativistic string model are presented.

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21

Negro, S., and F. Smirnov. "On one-point functions for sinh-Gordon model at finite temperature." Nuclear Physics B 875, no. 1 (October 2013): 166–85. http://dx.doi.org/10.1016/j.nuclphysb.2013.06.023.

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22

Teschner, J. "On the spectrum of the sinh-Gordon model in finite volume." Nuclear Physics B 799, no. 3 (August 2008): 403–29. http://dx.doi.org/10.1016/j.nuclphysb.2008.01.021.

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23

Takács, G. "Form factors of boundary exponential operators in the sinh-Gordon model." Nuclear Physics B 801, no. 3 (October 2008): 187–206. http://dx.doi.org/10.1016/j.nuclphysb.2008.01.025.

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24

Fring, A., G. Mussardo, and P. Simonetti. "Form factors for integrable lagrangian field theories, the sinh-Gordon model." Nuclear Physics B 393, no. 1-2 (March 1993): 413–41. http://dx.doi.org/10.1016/0550-3213(93)90252-k.

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25

Zamolodchikov, Al. "On the thermodynamic Bethe ansatz equation in the sinh-Gordon model." Journal of Physics A: Mathematical and General 39, no. 41 (September 27, 2006): 12863–87. http://dx.doi.org/10.1088/0305-4470/39/41/s09.

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26

Sergeev, Sergey. "Functional Bethe Ansatz for a sinh-Gordon Model with Real q." Symmetry 16, no. 8 (July 24, 2024): 947. http://dx.doi.org/10.3390/sym16080947.

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Recently, Bazhanov and Sergeev have described an Ising-type integrable model which can be identified as a sinh-Gordon-type model with an infinite number of states but with a real parameter q. This model is the subject of Sklyanin’s Functional Bethe Ansatz. We develop in this paper the whole technique of the FBA which includes: (1) Construction of eigenstates of an off-diagonal element of a monodromy matrix. The most important ingredients of these eigenstates are the Clebsh-Gordan coefficients of the corresponding representation. (2) Separately, we discuss the Clebsh-Gordan coefficients, as well as the Wigner’s 6j symbols, in details. The later are rather well known in the theory of 3D indices. Thus, the Sklyanin basis of the quantum separation of variables is constructed. The matrix elements of an eigenstate of the auxiliary transfer matrix in this basis are products of functions satisfying the Baxter equation. Such functions are called usually the Q-operators. We investigate the Baxter equation and Q-operators from two points of view. (3) In the model considered the most convenient Bethe-type variables are the zeros of a Wronskian of two well defined particular solutions of the Baxter equation. This approach works perfectly in the thermodynamic limit. We calculate the distribution of these roots in the thermodynamic limit, and so we reproduce in this way the partition function of the model. (4) The real parameter q, which is the standard quantum group parameter, plays the role of the absolute temperature in the model considered. Expansion with respect to q (tropical expansion) gives an alternative way to establish the structure of the eigenstates. In this way we classify the elementary excitations over the ground state.

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27

Salvo, Emanuele Di, and Dirk Schuricht. "Quantum quenches in the sinh-Gordon and Lieb–Liniger models." Journal of Statistical Mechanics: Theory and Experiment 2023, no. 5 (May 1, 2023): 053107. http://dx.doi.org/10.1088/1742-5468/acd2c3.

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Abstract The non-relativistic limit of integrable field theories at equilibrium has been intensively studied in the previous years; the simplest non-trivial case relates the sinh-Gordon model to the Lieb–Liniger model (LLM). Here we study this non-relativistic limit out of equilibrium, namely in the time evolution after a quantum quench. The obtained results agree with the known ones for the LLM, thus showing that the non-relativistic limit is applicable in this out-of-equilibrium setting.

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28

Alrebdi, Haifa I., Nauman Raza, Saima Arshed, Asma Rashid Butt, Abdel-Haleem Abdel-Aty, Clemente Cesarano, and Hichem Eleuch. "A Variety of New Explicit Analytical Soliton Solutions of q-Deformed Sinh-Gordon in (2+1) Dimensions." Symmetry 14, no. 11 (November 16, 2022): 2425. http://dx.doi.org/10.3390/sym14112425.

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In this paper, the (2+1)-dimensional q-deformed Sinh-Gordon model has been investigated via (G′G,1G)-expansion and Sine-Gordon-expansion methods. These techniques successfully retrieve trigonometric as well as hyperbolic solutions, along necessary restricted conditions applied on parameters. In addition to these solutions, dark solitons and complexiton solutions have also been obtained. The proposed equation expands the possibilities for modeling physical systems in which symmetry is broken. The obtained solutions are graphically illustrated. A Painlevé analysis for the proposed model has also been discussed in this paper.

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29

MUSSARDO, G. "FORM FACTORS IN OFF-CRITICAL SUPERCONFORMAL MODELS." International Journal of Modern Physics B 13, no. 24n25 (October 10, 1999): 2961–72. http://dx.doi.org/10.1142/s0217979299002794.

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We discuss the determination of the lowest Form Factors relative to the trace operators of N = 1 Super Sinh-Gordon Model. Analytic continuations of these Form Factors as functions of the coupling constant allows the study of interesting models in a uniform way, among these the latest model of the Roaming Series and a class of minimal supersymmetric models.

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30

Faquir, M., M. A. Manna, and A. Neveu. "An integrable equation governing short waves in a long-wave model." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2084 (June 5, 2007): 1939–54. http://dx.doi.org/10.1098/rspa.2007.1861.

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The dynamics of a nonlinear and dispersive long surface capillary-gravity wave model equation is studied analytically in its short-wave limit. We exhibit its Lax pair and some non-trivial conserved quantities. Through a change of functions, an unexpected connection between this classical surface water-wave model and the sine-Gordon (or sinh-Gordon) equation is established. Numerical and analytical studies show that in spite of integrability their solutions can develop singularities and multivaluedness in finite time. These features can be traced to the fact that the surface tension term in the energy involves second-order derivatives. It would be interesting to see in an experiment whether such singularities actually appear, for which surface tension would be specifically responsible.

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31

CHENAGHLOU, A. "ON THE QUANTUM REFLECTION FACTOR FOR THE SINH–GORDON MODEL WITH GENERAL BOUNDARY CONDITIONS." International Journal of Modern Physics A 15, no. 29 (November 20, 2000): 4623–54. http://dx.doi.org/10.1142/s0217751x0000224x.

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The one loop quantum corrections to the classical reflection factor of the sinh–Gordon model are calculated partially for general boundary conditions. The model is studied under boundary conditions which are compatible with integrability, and in the framework of the conventional perturbation theory generalized to the affine Toda field theory. It is found that the general form of the related quantum corrections are hypergeometric functions.

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32

Yan, J., and X. M. Qiu. "Sinh-Gordon Matter Field and a Solvable Model in Two-Dimensional Gravity." General Relativity and Gravitation 30, no. 9 (September 1998): 1319–29. http://dx.doi.org/10.1023/a:1018896306852.

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33

Gomes, J. F., L. H. Ymai, and A. H. Zimerman. "Integrablility of a classicalN= 2 super sinh-Gordon model with jump defects." Journal of High Energy Physics 2008, no. 03 (March 3, 2008): 001. http://dx.doi.org/10.1088/1126-6708/2008/03/001.

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34

Lukyanov, Sergei. "Finite temperature expectation values of local fields in the sinh-Gordon model." Nuclear Physics B 612, no. 3 (October 2001): 391–412. http://dx.doi.org/10.1016/s0550-3213(01)00365-0.

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35

Korepin, V. E., and N. A. Slavnov. "The determinant representation for quantum correlation functions of the sinh-Gordon model." Journal of Physics A: Mathematical and General 31, no. 46 (November 20, 1998): 9283–95. http://dx.doi.org/10.1088/0305-4470/31/46/018.

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36

Lu, Dianchen, Aly R. Seadawy, and M. Arshad. "Solitary wave and elliptic function solutions of sinh-Gordon equation and its applications." Modern Physics Letters B 33, no. 35 (December 16, 2019): 1950436. http://dx.doi.org/10.1142/s0217984919504360.

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The [Formula: see text]-Gordon model is an important model in special nonlinear partial differential equations (PDEs) which is arising in solid-state physics, mathematical physics, fluid dynamics, fluid flow, differential geometry, quantum theory, etc. The exact solutions in the type of solitary wave and elliptic functions solutions are created of [Formula: see text]-Gordon model by employing modified direct algebraic scheme. Moments of a few solutions are also depicted graphically. These solutions helps the physicians and mathematicians to understand the physical phenomena of this model. This technique can be utilized on other models to launch further exclusively novel solutions for other categories of nonlinear PDEs occurring in mathematical Physics.

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37

CHENAGHLOU, A., and E. CORRIGAN. "FIRST ORDER QUANTUM CORRECTIONS TO THE CLASSICAL REFLECTION FACTOR OF THE SINH–GORDON MODEL." International Journal of Modern Physics A 15, no. 28 (November 10, 2000): 4417–32. http://dx.doi.org/10.1142/s0217751x0000183x.

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The sinh–Gordon model is restricted to a half-line by boundary conditions maintaining integrability. A perturbative calculation of the reflection factor is given to one loop order in the bulk coupling and to first order in the difference of the two parameters introduced at the boundary, providing a further verification of Ghoshal's formula. The calculation is consistent with a conjecture for the general dependence of the reflection factor on the boundary parameters and the bulk coupling.

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38

CHENAGHLOU, A. "SECOND ORDER QUANTUM CORRECTIONS TO THE CLASSICAL REFLECTION FACTOR OF THE SINH–GORDON MODEL." International Journal of Modern Physics A 16, no. 28 (November 10, 2001): 4613–36. http://dx.doi.org/10.1142/s0217751x01005572.

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The sinh–Gordon model on a half-line with integrable boundary conditions is considered in low order perturbation theory developed in affine Toda field theory. The quantum corrections to the classical reflection factor of the model are studied up to the second order in the difference of the two boundary parameters and to one loop order in the bulk coupling. It is noticed that the general form of the second order quantum corrections are consistent with Ghoshal's formula.

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39

BRACKEN, PAUL. "A STRING MODEL FOR D-DIMENSIONAL DE SITTER SPACE–TIME AND EQUATIONS OF MOTION." International Journal of Modern Physics A 20, no. 26 (October 20, 2005): 6065–81. http://dx.doi.org/10.1142/s0217751x0502553x.

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De Sitter space–time is considered to be represented by a D-dimensional hyperboloid embedded in (D+1)-dimensional Minkowski space–time. The string equation is derived from a string action which contains a Lagrange multiplier to restrict coordinates to de Sitter space–time. The string system of equations is equivalent to a type of generalized sinh–Gordon equation. The evolution equations for all the variables including the coordinates and their derivatives are obtained for D=2,3 and 4.

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40

Klotzek, Andreas, and Michael Thies. "Kink dynamics, sinh-Gordon solitons and strings in AdS3from the Gross–Neveu model." Journal of Physics A: Mathematical and Theoretical 43, no. 37 (July 30, 2010): 375401. http://dx.doi.org/10.1088/1751-8113/43/37/375401.

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41

Raheel, M., Khalid K. Ali, Asim Zafar, Ahmet Bekir, Omar Abu Arqub, and Marwan Abukhaled. "Exploring the Analytical Solutions to the Economical Model via Three Different Methods." Journal of Mathematics 2023 (April 22, 2023): 1–15. http://dx.doi.org/10.1155/2023/1416097.

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In this article, the analytical solutions of economically important model named as the Ivancevic option pricing model (IOPM) along new definition of derivative have been explored. For this purpose, exp a function, extended sinh-Gordon equation expansion (EShGEE) and extended G ′ / G -expansion methods have been utilized. The resulting solutions are dark, bright, dark-bright, periodic, singular, and other kinds of solutions. These solutions are obtained and also verified by a Mathematica tool. Some of the gained results are explained by 2-D, 3-D, and contour plots.

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42

TARASOV, V. F. "ON EXACT HYPERGEOMETRIC SOLUTIONS OF CERTAIN SOLITON-LIKE EQUATIONS." International Journal of Modern Physics B 24, no. 23 (September 20, 2010): 4509–19. http://dx.doi.org/10.1142/s0217979210056645.

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It is shown that certain nonlinear wave evolution equations in (1+1)-dimensional space-time in the soliton theory: sine-Gordon (SG), sinh-Gordon (ShG), the nonlinear Schrödinger equation (NLS), the φ4 equation in quantum field theory, the Burgers diffusion equation (Brg) and the Huxley equation (Hsl) in biophysics, the Boussinesq equation (Bsq), can be solved in terms of hypergeometric functions of pFq-type. Such approach allows to establish the connection between "model" equations and simple functional relations (in the form of diagrams) of these functions; the latter gives the possibility to consider a number of "inverse problems" in the soliton theory in a new way and to get new "models" of solitary waves.

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43

HOU, BO-YU, and WEN-LI YANG. "THE DRESSING TRANSFORMATION OF THE CONFORMAL AFFINE TODA." International Journal of Modern Physics A 09, no. 17 (July 10, 1994): 2997–3006. http://dx.doi.org/10.1142/s0217751x94001187.

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We study the dressing transformations of the conformal affine [Formula: see text] Todal which can be obtained from a Hamiltonian reduction. As a special case, we obtain the dressing transformations of the sinh-Gordon model. We will show that the dressing group is the semiclassical limit of the quantum group [Formula: see text]. We will also obtain the algebra of the charges which generate the infinitesimal dressing transformations.

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44

Ali, Khalid K., Haifa I. Alrebdi, Norah A. M. Alsaif, Abdel-Haleem Abdel-Aty, and Hichem Eleuch. "Analytical Solutions for a New Form of the Generalized q-Deformed Sinh–Gordon Equation: ∂2u∂z∂ζ=eαu[sinhq(uγ)]p−δ." Symmetry 15, no. 2 (February 10, 2023): 470. http://dx.doi.org/10.3390/sym15020470.

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In this article, a new version of the generalized q-deformed Sinh–Gordon equation is presented, and analytical solutions are developed for specific parameter sets using those equations. There is a possibility that the new equation can be used to model physical systems that have broken symmetries and include also effects related to amplification or dissipation. In addition, we have include some illustrations that depict the varied patterns of soliton propagation.

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45

Bertini, Bruno, Lorenzo Piroli, and Pasquale Calabrese. "Quantum quenches in the sinh-Gordon model: steady state and one-point correlation functions." Journal of Statistical Mechanics: Theory and Experiment 2016, no. 6 (June 2, 2016): 063102. http://dx.doi.org/10.1088/1742-5468/2016/06/063102.

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Baskonus, Haci Mehmet, Tukur Abdulkadir Sulaiman, and Hasan Bulut. "On the exact solitary wave solutions to the long-short wave interaction system." ITM Web of Conferences 22 (2018): 01063. http://dx.doi.org/10.1051/itmconf/20182201063.

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In this paper, the application of the simplified the extended sinh-Gordon equation expansion method to the long-short-wave interaction system. We successfully construct various solitary wave solutions to this nonlinear complex model. The long-short-wave interaction system describes the interaction between one long longitudinal wave and one short transverse wave propagating in a generalized elastic medium. The 2D and 3D surfaces to some of the obtained solutions are plotted.

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47

Bytsko, Andrei G., and Jörg Teschner. "Quantization of models with non-compact quantum group symmetry: modular XXZ magnet and lattice sinh-Gordon model." Journal of Physics A: Mathematical and General 39, no. 41 (September 27, 2006): 12927–81. http://dx.doi.org/10.1088/0305-4470/39/41/s11.

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48

Cuba, Guillermo, and Roman Paunov. "A note on the symplectic structure on the dressing group in the sinh-Gordon model." Physics Letters B 381, no. 1-3 (July 1996): 255–61. http://dx.doi.org/10.1016/0370-2693(96)00384-x.

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49

Jhangeer, Adil, Farheen Ibraheem, Tahira Jamal, Muhammad Bilal Riaz, and Atef Abdel Kader. "Computation of soliton structure and analysis of chaotic behaviour in quantum deformed Sinh-Gordon model." PLOS ONE 19, no. 6 (June 21, 2024): e0304424. http://dx.doi.org/10.1371/journal.pone.0304424.

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Soliton dynamics and nonlinear phenomena in quantum deformation has been investigated through conformal time differential generalized form of q deformed Sinh-Gordon equation. The underlying equation has recently undergone substantial amount of research. In Phase 1, we employed modified auxiliary and new direct extended algebraic methods. Trigonometric, hyperbolic, exponential and rational solutions are successfully extracted using these techniques, coupled with the best possible constraint requirements implemented on parameters to ensure the existence of solutions. The findings, then, are represented by 2D, 3D and contour plots to highlight the various solitons’ propagation patterns such as kink-bright, bright, dark, bright-dark, kink, and kink-peakon solitons and solitary wave solutions. It is worth emphasizing that kink dark, dark peakon, dark and dark bright solitons have not been found earlier in literature. In phase 2, the underlying model is examined under various chaos detecting tools for example lyapunov exponents, multistability and time series analysis and bifurcation diagram. Chaotic behavior is investigated using various initial condition and novel results are obtained.

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Houwe, A., J. Sabi'u, G. Betchewe, M. Inc, and S. Y. Doka. "Modulation analysis and optical solitons of perturbed nonlinear Schrodinger equation." Revista Mexicana de Física 67, no. 4 Jul-Aug (June 8, 2021): 040705. http://dx.doi.org/10.31349/revmexfis.67.040705.

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We investigate modulation analysis and optical solitons of perturbed nonlinear Schrodinger equation (PNLSE). The PNLSE has terms of cubic nonlinearity and self-steepening and spatio-temporal dispersion (STD). Proposed model has been studied by [14, 15] without self-steepening term. The presence of the STD and self-steepening can help to compensate the low GVD to the model. Bright and dark solitary waves, trigonometric, periodic andsingular optical solitons are obtained by some expansion methods including exponential and sinh-Gordon. Obtained results will hold a significant place in the field of nonlinear optical fibers, where solitons are used to codify data.

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