Two numerical methods for the Zakharov-Rubenchik equations

Abstract

Two numerical methods are presented for the approximation of the Zakharov-Rubenchik equations (ZRE). The first one is the finite difference integrator Fourier pseudospectral method (FFP), which is implicit and of the optimal convergent rate at the order of O(N−r + τ2) in the discrete L2 norm without any restrictions on the grid ratio. The second one is to use the Fourier pseudospectral approach for spatial discretization and exponential wave integrator for temporal integration. Fast Fourier transform is applied to the discrete nonlinear system to speed up the numerical computation. Numerical examples are given to show the efficiency and accuracy of the new methods.