New traveling wave exact solutions to the coupled Klein–Gordon system of equations

Abstract

A system of coupled Klein–Gordon nonlinear partial differential equations are considered in this paper and several new families of exact solutions for this system are derived. Since this system is highly nonlinear, exact solutions are very difficult to obtain. A rational ansatz form is assumed to derive the required exact solutions in terms of the doubly periodic functions. We derive all the possible real solutions having this ansatz form and which are functions of Jacobi elliptic functions. Particular solutions corresponding to each family of solutions are presented graphically.