Exact three-wave solutions for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mrow><mml:mo>(</mml:mo><mml:mn>3</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-dimensional Jimbo–Miwa equation

Li, Zitian; Dai, Zhengde; Liu, Jun

doi:10.1016/j.camwa.2010.08.070

Cited by 29 publications

(2 citation statements)

References 9 publications

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“…where Θ 5 and Θ 6 are integral constants. Substituting Equations (5) and (13) into Equation (2) with the constraint (t) = 6 (t) Θ 0 , the fifth breather wave solution for Equation (1) is written as follows:…”

Section: Breather Wave Solutionsmentioning

confidence: 99%

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Breather wave solutions for the Kadomtsev‐Petviashvili equation with variable coefficients in a fluid based on the variable‐coefficient three‐wave approach

Liu

Zhu

Zhou

2019

Math Methods in App Sciences

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Herein, the Kadomtsev-Petviashvili equation with variable coefficients is investigated, which describes the long waves with small amplitude and slow dependence on the transverse coordinate in a single-layer shallow fluid. Breather wave solutions are obtained based on a variable-coefficient three-wave approach.The dynamical behaviors of the obtained solutions are graphically discussed for different choices of the free parameters in these solutions. KEYWORDS dynamical behavior, breather wave solutions, Kadomtsev-Petviashvili equation, variable-coefficient three-wave approach MSC CLASSIFICATION 35C08; 68M07; 33F10 wileyonlinelibrary.com/journal/mma

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Section: Breather Wave Solutionsmentioning

confidence: 99%

“…[2][3][4][5][6][7][8] Recently, considerable efforts were introduced to seek the exact solutions of nonlinear partial differential equations (NPDEs) via the three-wave approach. [9][10][11][12][13][14][15] This method was used to deal with the NPDEs when their coefficients were constants.…”

Section: Introductionmentioning

confidence: 99%

Breather wave solutions for the Kadomtsev‐Petviashvili equation with variable coefficients in a fluid based on the variable‐coefficient three‐wave approach

Liu

Zhu

Zhou

2019

Math Methods in App Sciences

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New exact solutions to extended (3 + 1)‐dimensional Jimbo‐Miwa equations by using bilinear forms

Kaur

Wazwaz

2018

Math Methods in App Sciences

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In this work, we investigate extended (3 + 1)‐dimensional Jimbo‐Miwa equations by locating movable critical points with the aid of Painlevé analysis. We construct bilinear forms through using truncated Painlevé expansions along with the Bell polynomials approach. The proposed approach provides enough freedom to construct solutions that may be related to large variety of real physical phenomena, and in addition, this approach enriches the solution structure. Abundant exact solutions involving various arbitrary constants are furnished in uniform manner by using test function. The obtained solutions are entirely new and different from those reported in the literature.

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Dromion-like soliton interactions for nonlinear Schrödinger equation with variable coefficients in inhomogeneous optical fibers

et al. 2019

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Exact three-wave solutions for the(3+1)-dimensional Jimbo–Miwa equation

Cited by 29 publications

References 9 publications

Breather wave solutions for the Kadomtsev‐Petviashvili equation with variable coefficients in a fluid based on the variable‐coefficient three‐wave approach

Breather wave solutions for the Kadomtsev‐Petviashvili equation with variable coefficients in a fluid based on the variable‐coefficient three‐wave approach

New exact solutions to extended (3 + 1)‐dimensional Jimbo‐Miwa equations by using bilinear forms

Dromion-like soliton interactions for nonlinear Schrödinger equation with variable coefficients in inhomogeneous optical fibers

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