Multi-soliton solutions and Breathers for the generalized coupled nonlinear Hirota equations via the Hirota method

Jia, Ting-Ting; Chai, Yi; Hao, Hui-Qin

doi:10.1016/j.spmi.2016.10.091

Cited by 87 publications

(13 citation statements)

References 18 publications

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“…Step Step 3: Substituting Equations ( 30) and (31) into Equation (17), then setting the coefficients of [R(ξ)] f [R (ξ)] i , for ( f = 0, 1, 2, . .…”

Section: Addendum To Kudryashov's Methods (Akm) For (2 + 1)-dimensional Hirota-maccari Equationmentioning

confidence: 99%

“…where σ 0 , and σ 1 are constants and σ 1 = 0. Substituting Equations ( 34) and (31) into Equation (17) and collecting all the transactions of this term [R(ξ)] l [R (ξ)] f , for (l = 0, 1, 2, . .…”

Section: Addendum To Kudryashov's Methods (Akm) For (2 + 1)-dimensional Hirota-maccari Equationmentioning

confidence: 99%

“…The approach by Painlevé has been applied successfully to construct the general solutions of certain nonlinear second-order equations [27]. Other methods that have been introduced include a new unified algebraic method [29], Weierstrass elliptic function expansion method [30] and extended trial method [31].…”

Section: Introductionmentioning

confidence: 99%

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Traveling Wave Solutions to the Nonlinear Evolution Equation Using Expansion Method and Addendum to Kudryashov’s Method

Alotaibi

2021

Symmetry

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The inspection of wave motion and propagation of diffusion, convection, dispersion, and dissipation is a key research area in mathematics, physics, engineering, and real-time application fields. This article addresses the generalized dimensional Hirota–Maccari equation by using two different methods: the exp(−φ(ζ)) expansion method and Addendum to Kudryashov’s method to obtain the optical traveling wave solutions. By utilizing suitable transformations, the nonlinear pdes are transformed into odes. The traveling wave solutions are expressed in terms of rational functions. For certain parameter values, the obtained optical solutions are described graphically with the aid of Maple 15 software.

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“…Step Step 3: Substituting Equations ( 30) and (31) into Equation (17), then setting the coefficients of [R(ξ)] f [R (ξ)] i , for ( f = 0, 1, 2, . .…”

Section: Addendum To Kudryashov's Methods (Akm) For (2 + 1)-dimensional Hirota-maccari Equationmentioning

confidence: 99%

Section: Addendum To Kudryashov's Methods (Akm) For (2 + 1)-dimensional Hirota-maccari Equationmentioning

confidence: 99%

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Traveling Wave Solutions to the Nonlinear Evolution Equation Using Expansion Method and Addendum to Kudryashov’s Method

Alotaibi

2021

Symmetry

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“…Furthermore, these can be utilized to estimate the boundary data that are used in numeric and semi-analytic methods. Such techniques include the Kudryashov method and its modifications [18][19][20], functional variable method [19], generalized Riccati equation mapping method [21], Jacobi elliptic function method [21,22], sine-Gordon expansion method [23], Hirota method [24], subequation method [25], soliton ansatz method [26], G /G-expansion method [27], new extended direct algebraic method [28], extended trial function method [29], new generalized exponential rational function method [30], integral dispersion equation method [31,32], modified extended tanh-function method [33], simple equation method [34,35], and modified simple equation methods [36] (see also the references that appear therein).…”

Section: Introductionmentioning

confidence: 99%

Stable Optical Solitons for the Higher-Order Non-Kerr NLSE via the Modified Simple Equation Method

et al. 2021

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This paper studies the propagation of the short pulse optics model governed by the higher-order nonlinear Schrödinger equation (NLSE) with non-Kerr nonlinearity. Exact one-soliton solutions are derived for a generalized case of the NLSE with the aid of software symbolic computations. The modified Kudryashov simple equation method (MSEM) is employed for this purpose under some parametric constraints. The computational work shows the difference, effectiveness, reliability, and power of the considered scheme. This method can treat several complex higher-order NLSEs that arise in mathematical physics. Graphical illustrations of some obtained solitons are presented.

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“…To our knowledge, Gramian solutions and interaction among the three solitons for equation (1.1) have not been proposed. In §2, with symbolic computation [32,33,[37][38][39][40][41][42][43][44][45][46][47], we give the N-soliton solutions in the Gramian for equation (1.1), where N = 1, 2, 3 . .…”

Section: Introductionmentioning

confidence: 99%

Gramian solutions and soliton interactions for a generalized (3 + 1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation in a plasma or fluid

Chen

Tian

2019

Proc. R. Soc. A.

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Plasmas and fluids are of current interest, supporting a variety of wave phenomena. Plasmas are believed to be possibly the most abundant form of visible matter in the Universe. Investigation in this paper is given to a generalized (3 + 1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation for the nonlinear phenomena in a plasma or fluid. Based on the existing bilinear form, N -soliton solutions in the Gramian are derived, where N = 1, 2, 3…. With N = 3, three-soliton solutions are constructed. Fission and fusion for the three solitons are presented. Effects of the variable coefficients, i.e. h ( t ), l ( t ), q ( t ), n ( t ) and m ( t ), on the soliton fission and fusion are revealed: soliton velocity is related to h ( t ), l ( t ), q ( t ), n ( t ) and m ( t ), while the soliton amplitude cannot be affected by them, where t is the scaled temporal coordinate, h ( t ), l ( t ) and q ( t ) give the perturbed effects, and m ( t ) and n ( t ), respectively, stand for the disturbed wave velocities along two transverse spatial coordinates. We show the three parallel solitons with the same direction.

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Multi-soliton solutions and Breathers for the generalized coupled nonlinear Hirota equations via the Hirota method

Cited by 87 publications

References 18 publications

Traveling Wave Solutions to the Nonlinear Evolution Equation Using Expansion Method and Addendum to Kudryashov’s Method

Traveling Wave Solutions to the Nonlinear Evolution Equation Using Expansion Method and Addendum to Kudryashov’s Method

Stable Optical Solitons for the Higher-Order Non-Kerr NLSE via the Modified Simple Equation Method

Gramian solutions and soliton interactions for a generalized (3 + 1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation in a plasma or fluid

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