2001/01/16 by Peter D. Miller, P. D. Miller, Miller, P. D. +2
Physics and Astronomy · #Advanced Fiber Laser Technologies #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Pattern Formation and Solitons (nlin.PS) #nlin.PS #nlin.SI
paper · pdf · doi:10.48550/arxiv.nlin/0101027
22 Pages. To appear in SIAM J. Math. Anal
arxiv created 2001/01/16 · openalex publication_date 2001/01/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.