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 Schrödinger 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 I1 and I2 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.