Numerical studies on a novel split-step quadratic B-spline finite element method for the coupled Schrödinger–KdV equations

We propose a novel split-step quadratic B-spline finite element method for solving the initial-boundary value problem of the coupled Schrödinger–KdV equations. A full-discrete finite element scheme is constructed. The conserved properties of the full-discrete scheme are proved. Detailed numerical results show the efficiency of our scheme.