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Semi-implicit operator splitting Padé method for higher-order nonlinear Schrödinger equations. (English) Zbl 1102.65093
Summary: 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 is proven to be stable by linear stability analysis. Numerical experiments and comparisons are investigated to show the advantages and effectivity of the OSPD method. Some interesting collision behaviors are also observed.

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
35Q51 Soliton equations
Full Text: DOI
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