The time-splitting Fourier spectral method for the coupled Schrödinger–Boussinesq equations

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.