Weakly nonlinear wavepackets in the Korteweg–de Vries equation: the KdV/NLS connection

John P. Boyd and Guan-Yu Chen

Mathematics and Computers in Simulation (MATCOM), 2001, vol. 55, issue 4, 317-328

Abstract: If the initial condition for the Korteweg–de Vries (KdV) equation is a weakly nonlinear wavepacket, then its evolution is described by the nonlinear Schrödinger (NLS) equation. This KdV/NLS connection has been known for many years, but its various aspects and implications have been discussed only in asides. In this note, we attempt a more focused and comprehensive discussion including such as issues as the KdV-induced long wave pole in the nonlinear coefficient of the NLS equation, the derivation of NLS from KdV through perturbation theory, resonant effects that give the NLS equation a wide range of applicability, and numerical illustrations. The multiple scales/nonlinear perturbation theory is explicitly extended to two orders beyond that which yields the NLS equation; the wave envelope evolves under a generalized-NLS equation which is third order in space and quintically-nonlinear.

Keywords: Nonlinear wavepacket i.e. nonlinear-wave; Korteweg–de Vries equation; NLS equation (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:55:y:2001:i:4:p:317-328

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