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.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.