Investigation of solutions of the Pade-II equation by MEFM

Abstract

In this study, singular soliton, topological, nontopological and rational solutions of the Pade-II equation, which is a type of nonlinear partial differential equations, are obtained. By selecting the appropriate parameters, solutions were obtained which provided the equations. Two and three dimensional graphics of the solutionswere drawn. It appears that the resulting solution functions and graphics have similar features. Hyperbolic andtrigonometric functions were also seen to have the same properties in their graphs since they are periodic functionsat the same time. The obtained solutions were found by using the modified expansion method. All solutions usingthis method are controlled by the Mathematica software program which provides the Pade-II equation. Using themodified expansion function method, the nonlinear partial differential equation with travelling wave transformationtakes the form of nonlinear ordinary differential equation. According to the balancing principle, there are also thedegree of the solution function containing the exponential function.