Exact solutions for the generalized sine-Gordon and the generalized sinh-Gordon equations

The reliable tanh method is used to handle the generalized sine-Gordon and the generalized sinh-Gordon equations. Families of exact travelling wave solutions are formally derived. The method requires minimal algebra work and the obtained results include the solutions derived in others’ works.

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

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

[3]  Abdul-Majid Wazwaz,et al.  New solitary-wave special solutions with compact support for the nonlinear dispersive K(m, n) equations , 2002 .

[4]  Engui Fan,et al.  Generalized tanh Method Extended to Special Types of Nonlinear Equations , 2002 .

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

[6]  Abdul-Majid Wazwaz,et al.  Compactons dispersive structures for variants of the K(n,n) and the KP equations , 2002 .

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

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

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

[10]  M. Wadati,et al.  The Exact Solution of the Modified Korteweg-de Vries Equation , 1972 .

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

[12]  Wang Kelin,et al.  Exact solutions for two nonlinear equations. I , 1990 .

[13]  A. Wazwaz.  A study of nonlinear dispersive equations with solitary-wave solutions having compact support , 2001 .

[14]  K. Glasner.  Nonlinear preconditioning for diffuse interfaces , 2001 .

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

[16]  M. Wadati.  Introduction to solitons , 2001 .

[17]  Hyman,et al.  Compactons: Solitons with finite wavelength. , 1993, Physical review letters.

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

[19]  A. H. Khater,et al.  The tanh method, a simple transformation and exact analytical solutions for nonlinear reaction-diffusion equations , 2002 .

[20]  M. Wadati,et al.  The Modified Korteweg-de Vries Equation , 1973 .