Time–space Jacobi pseudospectral simulation of multidimensional Schrödinger equation

Abstract

In this paper, the authors investigate the collision of soliton waves for multidimensional nonlinear Schrödinger equation (NSE) using the time–space Jacobi pseudospectral method. The proposed method is established in both time and space to approximate the solutions and to prove the theory of error estimates and stability analysis for the equations. Using the Jacobi derivatives matrices the given problem is reduced to a system of nonlinear algebraic equations, which will be solved using Newton's Raphson method. For numerical experiments, the method is tested on a number of different examples to study the behavior of collision of two and more than two solitons waves and single soliton wave. Moreover, numerical solutions are demonstrated to justify the theoretical results. The rate of convergence of the proposed method is obtained up to six‐order. The proposed method also preserves mass and energy conservation laws. A comparison of the numerical and exact solutions is depicted in the form of figures and tables.