Exact solutions to the double sinh-gordon equation by the tanh method and a variable separated ODE method

New exact travelling wave solutions for the double sinh-Gordon equation and its generalized form are formally derived by using the tanh method and the variable separated ODE method. The Painleve property v = e^u is employed to support the tanh method in deriving exact solutions. The work emphasizes the power of the methods in providing distinct solutions of different physical structures.

[1]  Guo-Wei Wei,et al.  Discrete singular convolution for the sine-Gordon equation , 2000 .

[2]  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..

[3]  Abdul-Majid Wazwaz,et al.  The tanh method for traveling wave solutions of nonlinear equations , 2004, Appl. Math. Comput..

[4]  A. Polyanin,et al.  Handbook of Nonlinear Partial Differential Equations , 2003 .

[5]  Mark J. Ablowitz,et al.  Regular ArticleOn the Numerical Solution of the Sine–Gordon Equation: I. Integrable Discretizations and Homoclinic Manifolds , 1996 .

[6]  Abdul-Majid Wazwaz,et al.  Partial differential equations : methods and applications , 2002 .

[7]  I. Antoniou,et al.  Solitons and Chaos , 1992 .

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

[9]  G. Rowlands,et al.  Nonlinear Waves, Solitons and Chaos , 1990 .

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

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

[12]  Abdul-Majid Wazwaz,et al.  The variable separated ODE and the tanh methods for solving the combined and the double combined sinh-cosh-Gordon equations , 2006, Appl. Math. Comput..

[13]  L. Chambers.  Linear and Nonlinear Waves , 2000, The Mathematical Gazette.

[14]  Mark J. Ablowitz,et al.  On the Numerical Solution of the Sine-Gordon Equation , 1996 .

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

[16]  J. Perring,et al.  A Model unified field equation , 1962 .

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

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