New exact double periodic wave and complex wave solutions for a generalized sinh-Gordon equation

In this paper, dependent and independent variable transformations are introduced to solve a generalized sinh-Gordon equation by using the binary F-expansion method and the knowledge of elliptic equation and Jacobian elliptic functions. Many different new exact solutions such as double periodic wave and complex wave solutions are obtained. Some previous results are extended.

[1]  K. Chow A class of doubly periodic waves for nonlinear evolution equations , 2002 .

[2]  Emmanuel Yomba,et al.  A generalized auxiliary equation method and its application to nonlinear Klein–Gordon and generalized nonlinear Camassa–Holm equations , 2008 .

[3]  New exact solutions for the sinh-Gordon equation , 2006 .

[4]  P. Stevenhagen,et al.  ELLIPTIC FUNCTIONS , 2022 .

[5]  G. Lamb Elements of soliton theory , 1980 .

[6]  P. Drazin,et al.  Solitons: An Introduction , 1989 .

[7]  Ke Chen,et al.  Applied Mathematics and Computation , 2022 .

[8]  Yao Long,et al.  The binary F-expansion method and its application for solving the (n + 1)-dimensional sine-Gordon equation , 2009 .

[9]  Liang Gao,et al.  Bifurcations of traveling wave solutions for a generalized Sinh-Gordon equation , 2008 .

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

[11]  Liu Shi-da,et al.  Exact Jacobian Elliptic Function Solutions to sinh-Gordon Equation , 2006 .

[12]  Jibin Li,et al.  Bounded travelling wave solutions for the (n + 1)-dimensional sine- and sinh-Gordon equations , 2005 .

[13]  K. Narita,et al.  Deformed Sine- and Sinh-Gordon Equations, Deformed Liouville Equations, and Their Discrete Models , 2003 .

[14]  Double elliptic equation method and new exact solutions of the (n+1)-dimensional sinh-Gordon equation , 2007 .

[15]  Abdul-Majid Wazwaz,et al.  Exact solutions for the generalized sine-Gordon and the generalized sinh-Gordon equations , 2006 .