Semi-inverse Method to the Klein-Gordon Equation with Quadratic Nonlinearity

Nonlinear electrical and mechanical systems have been widely used in the industry electronics and consumer devices. Many numerical algorithms can be employed to obtain the numerical solutions of the nonlinear dynamics or electromagnetic equations. However, it takes a lot of time and decreases the solution accuracy. In this paper, a novel method, called Semi-Inverse Method, is proposed to seek solitary solutions of nonlinear differential equations. The Klein-Gordon equation with quadratic nonlinearity is selected to illustrate the effectiveness and simplicity of the suggested method.