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- W2111008786 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." @default.
- W2111008786 created "2016-06-24" @default.
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- W2111008786 date "2001-03-01" @default.
- W2111008786 modified "2023-09-23" @default.
- W2111008786 title "Weakly nonlinear wavepackets in the Korteweg–de Vries equation: the KdV/NLS connection" @default.
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- W2111008786 doi "https://doi.org/10.1016/s0378-4754(00)00291-3" @default.
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