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SIAM Journal on Mathematical Analysis
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Preprint . 2001
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SIAM Journal on Mathematical Analysis
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https://dx.doi.org/10.48550/ar...
Article . 2001
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An Exactly Solvable Model for the Interaction of Linear Waves with Korteweg--de Vries Solitons

An exactly solvable model for the interaction of linear waves with Korteweg--de Vries solitons
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2001Embargo end date: 01 Jan 2001 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Mathematical Analysis, volume 33, pages 261-285 (issn: 0036-1410, eissn: 1095-7154, Copyright policy )
Authors: Miller, P. D.; Clarke, S. R.;

doi: 10.1137/s0036141099365431 , 10.48550/arxiv.nlin/0101027

arXiv: nlin/0101027

An Exactly Solvable Model for the Interaction of Linear Waves with Korteweg--de Vries Solitons

Abstract

Under certain mode-matching conditions, small-amplitude waves can be trapped by coupling to solitons of nonlinear fields. We present a model for this phenomenon, consisting of a linear equation coupled to the Korteweg-de Vries equation. The model has one parameter, a coupling constant. For one value of the coupling constant the model becomes the linearized KdV equation. We solve the problem exactly for a different value of the coupling parameter, for which the solutions behave differently. We describe an application of our results to the dynamics of molecules.

22 Pages. To appear in SIAM J. Math. Anal

Related Organizations
Keywords

Soliton equations, Nonlinear Sciences - Exactly Solvable and Integrable Systems, wave trapping, FOS: Physical sciences, Completeness of sets of functions in one variable harmonic analysis, coupled systems, Pattern Formation and Solitons (nlin.PS), Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems, Nonlinear Sciences - Pattern Formation and Solitons, KdV equations (Korteweg-de Vries equations), Korteweg-de Vries equation, solitons, Exactly Solvable and Integrable Systems (nlin.SI), completeness relations

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
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bronze