Coupling of homotopy perturbation and modified Lindstedt–Poincaré methods for traveling wave solutions of the nonlinear Klein–Gordon equation

Abstract oupled method of He’s homotopy perturbation method and modified Lindstedt–Poincare method is applied to the search for traveling wave solutions of a variety of Klein–Gordon equations. The results obtained provide confirmation for the validity of the coupled method.

[1]  W. Hereman,et al.  The tanh method: I. Exact solutions of nonlinear evolution and wave equations , 1996 .

[2]  C. Lim,et al.  A new approximate analytical approach for dispersion relation of the nonlinear Klein-Gordon equation. , 2001, Chaos.

[3]  Ji-Huan He,et al.  Modified Lindstedt–Poincare methods for some strongly non-linear oscillations: Part I: expansion of a constant , 2002 .

[4]  M. A. Abdou.  APPROXIMATE SOLUTIONS OF NONLINEAR DIFFERENTIAL DIFFERENCE EQUATIONS , 2009 .

[5]  W. Hereman,et al.  The tanh method: II. Perturbation technique for conservative systems , 1996 .

[6]  Roger Knobel,et al.  An introduction to the mathematical theory of waves , 1999 .

[7]  Ji-Huan He.  A coupling method of a homotopy technique and a perturbation technique for non-linear problems , 2000 .

[8]  W. Malfliet.  Solitary wave solutions of nonlinear wave equations , 1992 .

[9]  M. A. Abdou,et al.  The solution of a coupled system of nonlinear physical problems using the homotopy analysis method , 2009 .

[10]  K. Noor,et al.  SOLVING SECOND-ORDER SINGULAR PROBLEMS USING HES POLYNOMIALS , 2009 .

[11]  M. Noor,et al.  Traveling Wave Solutions of Seventh-order Generalized KdV Equations Using He's Polynomials , 2009 .

[12]  Hong-Mei Liu,et al.  Approximate period of nonlinear oscillators with discontinuities by modified Lindstedt–Poincare method , 2005 .

[13]  Ahmet Yildirim,et al.  Determination of limit cycles by a modified straightforward expansion for nonlinear oscillators , 2007 .

[14]  Muhammad Aslam Noor,et al.  Homotopy Perturbation Method for Solving Partial Differential Equations , 2009 .

[15]  Ahmet Yildirim,et al.  A note on He’s homotopy perturbation method for van der Pol oscillator with very strong nonlinearity , 2007 .

[16]  M. Noor,et al.  Variational Iteration Method for Solving Higher-order Nonlinear Boundary Value Problems Using He's Polynomials , 2008 .

[17]  S. Mohyud-Din,et al.  Parameter-expansion Techniques for Strongly Nonlinear Oscillators , 2009 .

[18]  G. Whitham.  A general approach to linear and non-linear dispersive waves using a Lagrangian , 1965, Journal of Fluid Mechanics.

[19]  Ji-Huan He.  Homotopy perturbation technique , 1999 .

[20]  Abdul-Majid Wazwaz,et al.  Travelling wave solutions for combined and double combined sine-cosine-Gordon equations by the variable separated ODE method , 2006, Appl. Math. Comput..

[21]  Ji-Huan He.  SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS , 2006 .

[22]  Sun Jiong,et al.  A direct method for solving sine-Gordon type equations , 2002 .

[23]  K. Noor,et al.  On the Coupling of He's Polynomials and Laplace Transformation , 2010 .

[24]  M. A. Abdou.  New applications of He's homotopy perturbation method for nonlinear differential difference equations , 2009 .

[25]  Vimal Singh,et al.  Perturbation methods , 1991 .

[26]  Abdul-Majid Wazwaz,et al.  The tanh method: exact solutions of the sine-Gordon and the sinh-Gordon equations , 2005, Appl. Math. Comput..

[27]  Samuel S. P. Shen,et al.  A Course on Nonlinear Waves , 1993 .

[28]  M. Noor,et al.  Some Relatively New Techniques for Nonlinear Problems , 2009 .

[29]  Syed Tauseef Mohyud-Din,et al.  Traveling wave solutions of Whitham–Broer–Kaup equations by homotopy perturbation method , 2010 .

[30]  M. A. Abdou,et al.  New Applications of the Homotopy Analysis Method , 2008 .

[31]  Ahmet Yildirim,et al.  Determination of periodic solution for a u1/3 force by He's modified Lindstedt–Poincaré method , 2007 .

[32]  Muhammad Aslam Noor,et al.  Homotopy Perturbation Method for Solving Fourth-Order Boundary Value Problems , 2007 .

[33]  Zuntao Fu,et al.  Exact Solutions to Double and Triple Sinh-Gordon Equations , 2004 .