An Exactly Solvable Model for the Interaction of Linear Waves with Korteweg-de Vries Solitons
Abstract
Description
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
22 Pages. To appear in SIAM J. Math. Anal