Traveling wave solutions to the ( n + 1 ) -dimensional sinh–cosh–Gordon equation

• Published in: Computers & mathematics with applications (1987) Vol. 61; no. 3; pp. 699 - 707
• Main Authors: Fan, Xinghua, Yang, Shouxiang, Yin, Jiuli, Tian, Lixin
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-02-2011
• Subjects: Dynamical systems; Generalized sinh–cosh–Gordon equation; Hyperbolic functions; Kink solution; Kink-like wave solution; Mathematical analysis; Mathematical models; Partial differential equations; Periodic wave solution; Solitary wave solution; Solitary waves; Traveling waves; Kink-like wave solution; Periodic wave solution; Generalized sinh–cosh–Gordon equation; Kink solution; Solitary wave solution
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2010.12.017

Traveling wave solutions for a generalized sinh–cosh–Gordon equation are studied. The equation is transformed into an auxiliary partial differential equation without any hyperbolic functions. By using the theory of planar dynamical system, the existence of different kinds of traveling wave solutions of the auxiliary equation is obtained, including smooth solitary wave, periodic wave, kink and antikink wave solutions. Some explicit expressions of the blow-up solution, kink-like solution, antikink-like solution and periodic wave solution to the generalized sinh–cosh–Gordon equation are given. Planar portraits of the solutions are shown.