One and two soliton solutions for the sinh-Gordon equation in (1+1), (2+1) and (3+1) dimensions

Abstract In this work we study the nonlinear sinh–Gordon equation in (1+1), (2+1) and (3+1) dimensions. We use the simplified form of Hirota’s method, to derive one and two soliton solutions for each equation.

[1]  Abdul-Majid Wazwaz,et al.  Multiple-front solutions for the Burgers equation and the coupled Burgers equations , 2007, Appl. Math. Comput..

[2]  Ryogo Hirota,et al.  Exact Three-Soliton Solution of the Two-Dimensional Sine-Gordon Equation , 1973 .

[3]  Abdul-Majid Wazwaz,et al.  Travelling wave solutions for the MKdV-sine-Gordon and the MKdV-sinh-Gordon equations by using a variable separated ODE method , 2006, Appl. Math. Comput..

[4]  Abdul-Majid Wazwaz,et al.  Multiple-soliton solutions for the Boussinesq equation , 2007, Appl. Math. Comput..

[5]  Abdul-Majid Wazwaz,et al.  M-component nonlinear evolution equations: multiple soliton solutions , 2010 .

[6]  Anjan Biswas,et al.  1-Soliton solution of the B(m,n) equation with generalized evolution , 2009 .

[7]  Willy Hereman,et al.  Symbolic methods to construct exact solutions of nonlinear partial differential equations , 1997 .

[8]  Abdul-Majid Wazwaz,et al.  New solitons and kink solutions for the Gardner equation , 2007 .

[9]  Abdul-Majid Wazwaz,et al.  Exact solutions to the double sinh-gordon equation by the tanh method and a variable separated ODE method , 2005 .

[10]  Mehdi Dehghan,et al.  Boundary element solution of the two-dimensional sine-Gordon equation using continuous linear elements , 2009 .

[11]  Abdul-Majid Wazwaz,et al.  The variable separated ODE method for travelling wave solutions for the Boussinesq-double sine-Gordon and the Boussinesq-double sinh-Gordon equations , 2006, Math. Comput. Simul..

[12]  A. Wazwaz Partial Differential Equations and Solitary Waves Theory , 2009 .

[13]  Zhongying Chen,et al.  Multilevel augmentation methods for solving the sine-Gordon equation , 2011 .

[14]  広田 良吾,et al.  The direct method in soliton theory , 2004 .

[15]  Abdul-Majid Wazwaz,et al.  Integrable (2+1)-dimensional and (3+1)-dimensional breaking soliton equations , 2010 .

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

[17]  A. Wazwaz The Hirota's direct method and the tanh-coth method for multiple-soliton solutions of the Sawada-Kotera-Ito seventh-order equation , 2008, Appl. Math. Comput..

[18]  Jarmo Hietarinta,et al.  A Search for Bilinear Equations Passing Hirota''s Three-Soliton Condition , 1987 .

[19]  Anjan Biswas,et al.  Bright and dark solitons of the generalized nonlinear Schrödinger’s equation , 2010 .