Meshless method for solving nonlinear Sine-Gordon equation

Abstract Sine-Gordon is a classical wave equation with a nonlinear sine source term. In this article, the method of approximate particular solution is applied to solve the nonlinear sine-Gordon equation. In the algorithm, the primary operator Laplacian is kept on the left, and other terms are placed on the right, regarded as forcing term. Therefore, the original equation can be regarded as a standard Poisson equation. Then, based on the theory of radial basis function interpolation, the solution of the original problem can be obtained by solving the operator equation. This method is meshless with advantages such as ease of implementation and high accuracy.