Abstract
In this article, two split-step finite difference methods for Schrödinger-KdV equations are formulated and investigated. The main features of our methods are based on: (i) The applications of split-step technique for Schrödinger-like equation in time. (ii) The utilizations of high-order finite difference method for KdV-like equation in spatial discretization. (iii) Our methods are of spectral-like accuracy in space and can be realized by fast Fourier transform efficiently. Numerical experiments are conducted to illustrate the efficiency and accuracy of our numerical methods.
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