Solutions of Three Dimensional Nonlinear Klein-Gordon Equations by Using Quadruple Laplace Transform

This study focuses on solving three-dimensional non-linear Klein-Gordon equations of four variables by using the quadruple Laplace transform method coupled with the iterative method. This study was designed in order to show the quadruple Laplace transform with an iterative method for solving three-dimensional nonlinear Klein-Gordon equations. The quadruple Laplace transform with the iterative method was aimed at getting analytical solutions of three-dimensional nonlinear Klein-Gordon equations. Exact solutions obtained through the iterative method have been analytically evaluated and presented in the form of a table and graph. The analytical solutions of these equations have been given in terms of convergent series with a simply calculable system, and the nonlinear terms in equations can easily be solved by the iterative method. Illustrative examples are also provided to demonstrate the applicability and efficiency of the method. The result renders the applicability and efficiency of the applied method. Finally, the quadruple Laplace transform and iterative method is an excellent method for the solution of nonlinear Klein-Gordon equations.