New exact solutions of the combined and double combined sinh-cosh-Gordon equations via modified Kudryashov method

The combined and double combined sinh-cosh-Gordon equations are very important to a wide range of various scientific applications that ranges from chemical reactions to water surface gravity waves. In this article, with the assistance of a function transform and Painlevè property, the nonlinear combined and double combined sinh-cosh-Gordon equations turn into ordinary differential equations. Later on, modified Kudryashov method is adopted for investigating new analytical solution of the studied equations. As a consequence, a series of new analytical solutions are acquired and we demonstrated the actual behavior of the achieved solutions of the mentioned equations with the aid of 3D and 2D MATLAB graphs. Finally, we also validate the effectiveness of the modified Kudryashov method for the problem of extracting new exact solutions of the combined and double combined sinh-cosh-Gordon equations with the aid of Maple package program. It is shown that the implemented method is capable to extract new solutions and it can also use to other nonlinear partial differential equation (NLPDE's) arising in mathematical physics or other applied field.