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The time-splitting Fourier spectral method for the coupled Schrödinger-Boussinesq equations. (English) Zbl 1245.35116

Summary: The periodic initial boundary value problem of the coupled Schrödinger-Boussinesq equations is studied by the time-splitting Fourier spectral method. A time-splitting spectral discretization for the Schrödinger-like equation is applied, while a Crank-Nicolson/leap-frog type discretization is utilized for time derivatives in the Boussinesq-like equation. Numerical tests show that the time-splitting Fourier spectral method provides high accuracy for the coupled Schrödinger-Boussinesq equations.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35Q35 PDEs in connection with fluid mechanics
65M22 Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs
65T50 Numerical methods for discrete and fast Fourier transforms
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