Explicit homoclinic tube solutions and chaos for Zakharov system with periodic boundary

Dai, Zhengde; Jian, Huang; Jiang, Murong

doi:10.1016/j.physleta.2005.12.026

Cited by 28 publications

(13 citation statements)

References 7 publications

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“…In recent years, quite a few methods for obtaining explicit traveling and solitary wave solutions of nonlinear evolution equations have been proposed. In recent years, exact homoclinic and heteroclinic solutions were proposed for some NEEs like nonlinear Schrödinger equation, Sine-Gordon equation, DaveyStewartson equation, Zakharov equation, and Boussinesq equation [1][2][3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Soliton Solutions of the Coupled Schrödinger-Boussinesq Equations for Kerr Law Nonlinearity

Jawad

Abu-AlShaeer

2018

Abstract and Applied Analysis

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In this paper, the coupled Schrödinger-Boussinesq equations (SBE) will be solved by the sech, tanh, csch, and the modified simplest equation method (MSEM). We obtain exact solutions of the nonlinear for bright, dark, and singular 1-soliton solution. Kerr law nonlinearity media are studied. Results have proven that modified simple equation method does not produce the soliton solution in general case. Solutions may find practical applications and will be important for the conservation laws for dispersive optical solitons.

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Section: Introductionmentioning

confidence: 99%

Soliton Solutions of the Coupled Schrödinger-Boussinesq Equations for Kerr Law Nonlinearity

Jawad

Abu-AlShaeer

2018

Abstract and Applied Analysis

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“…The existence of the homoclinic and heteroclinic orbits is very important for investigating the spatiotemporal chaotic behavior of the nonlinear evolution equations (NEEs). In recent years, exact homoclinic and heterclinic solutions were proposed for some NEEs like nonlinear Schrödinger equation, Sine-Gordon equation, Davey-Stewartson equation, Zakharov equation, and Boussinesq equation [1][2][3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Various Heteroclinic Solutions for the Coupled Schrödinger-Boussinesq Equation

Jiang

Dai

2013

Abstract and Applied Analysis

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“…Very recently, a new technique called "extended homoclinic test technique"was proposed [9] and has been applied to seek periodic solitary wave solutions of integrable equations [10,11]. In this work, we apply the technique to the (3+1)-dimensional KP equation.…”

Section: Introductionmentioning

confidence: 99%

New Periodic Solitary-Wave Solutions to the (3+1)- Dimensional Kadomtsev-Petviashvili Equation

Dai

2010

MCA

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Abstract-By the extended homoclinic test technique, explicit solutions of the (3+1)-dimensional Kadomtsev-Petviashvili(KP) equation are obtained. These solutions include doubly periodic wave solutions, doubly soliton solutions and periodic solitary-wave solutions. It is shown that the extended homoclinic test technique is a straightforward and powerful mathematical tool for solving nonlinear evolution equation.

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Explicit homoclinic tube solutions and chaos for Zakharov system with periodic boundary

Cited by 28 publications

References 7 publications

Soliton Solutions of the Coupled Schrödinger-Boussinesq Equations for Kerr Law Nonlinearity

Soliton Solutions of the Coupled Schrödinger-Boussinesq Equations for Kerr Law Nonlinearity

Various Heteroclinic Solutions for the Coupled Schrödinger-Boussinesq Equation

New Periodic Solitary-Wave Solutions to the (3+1)- Dimensional Kadomtsev-Petviashvili Equation

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