Exact solutions to the sine-Gordon-type equations

In this paper, the sine-Gordon-type equations, including single sine-Gordon equation, double sine-Gordon equation and triple sine-Gordon equation are studied by introducing certain dependent variable transformations and the projective Riccati equation method. Several new exact solutions are obtained.

[1]  Bin He,et al.  New exact solutions of the double sine-Gordon equation using symbolic computations , 2007, Appl. Math. Comput..

[2]  Yong Chen,et al.  General projective Riccati equation method and exact solutions for generalized KdV-type and KdV–Burgers-type equations with nonlinear terms of any order , 2004 .

[3]  Constantine A. Popov,et al.  Perturbation theory for the double sine-Gordon equation , 2003, nlin/0312054.

[4]  Robert Conte,et al.  Link between solitary waves and projective Riccati equations , 1992 .

[5]  P. C. Dash,et al.  Mixing exponential and double sine-Gordon equation , 2004 .

[6]  Lou Sen-yue,et al.  Solitary Wave Solutions of Triple Sine-Gordon Equation , 2004 .

[7]  Jian Zhang,et al.  Applications of the Jacobi elliptic function method to special-type nonlinear equations , 2002 .

[8]  Hong-qing Zhang,et al.  New exact solutions to the generalized coupled Hirota–Satsuma Kdv system , 2005 .

[9]  Zuntao Fu,et al.  New kinds of solutions to Gardner equation , 2004 .

[10]  Zhenya Yan,et al.  Generalized method and its application in the higher-order nonlinear Schrodinger equation in nonlinear optical fibres , 2003 .

[11]  Zuntao Fu,et al.  JACOBI ELLIPTIC FUNCTION EXPANSION METHOD AND PERIODIC WAVE SOLUTIONS OF NONLINEAR WAVE EQUATIONS , 2001 .

[12]  Zuntao Fu,et al.  Exact solutions to sine-Gordon-type equations , 2006 .

[13]  Zuntao Fu,et al.  New transformations and new approach to find exact solutions to nonlinear equations , 2002 .

[14]  Kwok Wing Chow,et al.  New interaction solutions of multiply periodic, quasi-periodic and non-periodic waves for the (n + 1)-dimensional double sine-Gordon equations , 2007 .