A conservative spectral method for the coupled Schrödinger-KdV equations

Hao Zhou, Danfu Han, Miaoyong Du and Yao Shi
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Hao Zhou: Department of Mathematics, Hangzhou Normal University, Hangzhou, 310006, P. R. China
Danfu Han: Department of Mathematics, Hangzhou Normal University, Hangzhou, 310006, P. R. China
Miaoyong Du: Department of Mathematics, Hangzhou Normal University, Hangzhou, 310006, P. R. China
Yao Shi: Department of Mathematics, Hangzhou Normal University, Hangzhou, 310006, P. R. China

International Journal of Modern Physics C (IJMPC), 2020, vol. 31, issue 05, 1-16

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, L∞ and L2 error norms. Numerical results manifest better performance of the scheme compared with other numerical schemes.

Keywords: Schrödinger-KdV equations; spectral collocation method; conservation; exponential time differencing; padé approximation; decoupled scheme (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0129183120500746

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