A conservative spectral method for the coupled Schrödinger-KdV equations

Abstract

In this work, we present a conservative method to solve the coupled Schrödinger-KdV (CSK) equations. The CSK equations are discretized in space by Fourier spectral collocation method and exponential time differencing with three-layer implicit schemes for time dependence. The scheme is decoupled and conserve semi-discrete three invariants. To demonstrate the accuracy and reliability of the used scheme, we use three invariants, [Formula: see text] and [Formula: see text] error norms. Numerical results manifest better performance of the scheme compared with other numerical schemes.