Travelling wave solutions for a nonlinear variant of the PHI-four equation

An analytic study on a complex nonlinear system (Coupled Higgs equation) and a nonlinear variant of the PHI-four equation is presented in this paper. The Exp-function method is employed to derive exact periodic and generalized solitary solutions of these equations. The solutions are compared with those obtained by the tanh method, the sine-cosine method and the Weierstrass elliptic function method, furthermore, new and more general solutions are found.

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“…Then, the travelling wave solutions of the following nonlinear equation named a variant of the PHI-four equation [37][38][39] are expressed by…”

Section: Introductionmentioning

confidence: 99%

New Exact and Explicit Travelling Wave Solutions for the Coupled Higgs Equation and a Nonlinear Variant of the PHI-four Equation

Khajeh¹,

Kabir²,

Koma³

2010

International Journal of Nonlinear Sciences and Numerical Simulation

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“…In this paper, by means of the He's variational approach, we will obtain some Solitary and periodic solutions of the following PHI-four equation given in [11] …”

Section: Introductionmentioning

confidence: 99%

Using He's variational method to seek the traveling wave solution of PHI-four equation

Najafi¹

2012

International Journal of Applied Mathematical Research

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In this paper, we established travelling wave solutions of the nonlinear equation. The He's variational method was used to construct travelling wave solutions of the PHI-four equation. The obtained results include periodic and solitary wave solutions. It is also shown that the He's variational method, with the help of symbolic computation, provides a powerful mathematical tool for solving other nonlinear evolution equations arising in mathematical physics.

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“…Up to now, many powerful methods to seek for exact solutions to the nonlinear differential equations have been proposed. Among these are inverse scattering method [1], Lie group method [2,3], bifurcation method of dynamical systems [4][5][6], sinecosine method [7,8], tanh function method [9][10][11], homogenous balance method [12], Weierstrass elliptic function method [13].…”

Section: Introductionmentioning

confidence: 99%

On Exact Traveling Wave Solutions for (1 + 1) Dimensional Kaup-Kupershmidt Equation

Feng¹,

Li²

2011

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Travelling wave solutions for a nonlinear variant of the PHI-four equation

Cited by 27 publications

References 16 publications

New Exact and Explicit Travelling Wave Solutions for the Coupled Higgs Equation and a Nonlinear Variant of the PHI-four Equation

New Exact and Explicit Travelling Wave Solutions for the Coupled Higgs Equation and a Nonlinear Variant of the PHI-four Equation

Using He's variational method to seek the traveling wave solution of PHI-four equation

On Exact Traveling Wave Solutions for (1 + 1) Dimensional Kaup-Kupershmidt Equation

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