An Exactly Solvable Model for the Interaction of Linear Waves with Korteweg--de Vries Solitons
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Publication:2753546
DOI10.1137/S0036141099365431zbMATH Open0987.35140arXivnlin/0101027MaRDI QIDQ2753546
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Publication date: 11 November 2001
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/nlin/0101027
KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Completeness of sets of functions in one variable harmonic analysis (42A65)
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