Application of tanh–coth method for combined and double combined sinh–cosh–Gordon equations arising from chemical reactions to water surface gravity waves

An application of the generalized tanh–coth method to search for exact solutions of nonlinear partial differential equations is analyzed. This method is used for the combined and the double combined sinh-cosh-Gordon equations. The generalized tanh–coth method was used to construct periodic wave and solitary wave solutions of nonlinear evolution equations. This method is developed for searching for exact travelling wave solutions of nonlinear partial differential equations. It is shown that the generalized tanh-coth method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear problems.