Semi-implicit operator splitting Padé method for higher-order nonlinear Schrödinger equations

We propose a semi-implicit finite difference operator splitting Padé (OSPD) method for solving the higher-order nonlinear Schrödinger equation which describes the optical soliton wave propagation in fibers. The method achieves fourth order of accuracy in space and has been proven to be stable by linear stability analysis. Numerical experiments and comparisons are investigated to show the advantages and effectivity of the OSPD method. And some interesting collision behaviors are also observed.