The variable separated ODE and the tanh methods for solving the combined and the double combined sinh–cosh-Gordon equations

摘要

Exact travelling wave solutions for the combined sinh–cosh-Gordon and the double combined sinh–cosh-Gordon equation are formally derived. The Painlevé property v = eu will be used to back up the tanh method to derive a first set of solutions. The newly developed variable separated ODE method is also used to derive a second set of solutions. Each method provides travelling wave solutions of distinct physical structures.