Cubic B-spline Galerkin method for numerical solution of the coupled nonlinear Schrödinger equation

Abstract In this paper, the Galerkin method, based on cubic B-spline function as the shape and weight functions is applied for the numerical solution of the one-dimensional coupled nonlinear Schrodinger equation. Numerical experiments involving single solitary wave, collision of two solitary waves and collision of three solitary waves are conducted. The obtained numerical results of the proposed scheme are compared with the analytical results and previously published numerical results. Two conserved quantities I 1 and I 2 are calculated for collision of two solitary waves and interaction of three solitary waves. The scheme provides accurate results which are in good agreement when compared to other numerical schemes. The order of convergence of the scheme is calculated. Moreover, the use of cubic B-spline Galerkin method produces smooth solutions without numerical smearing.