Exact solutions of the 3-wave resonant interaction equation

A. Degasperis, S. Lombardo

Research output: Contribution to JournalArticleAcademicpeer-review


The Darboux-Dressing Transformations are applied to the Lax pair associated to the system of nonlinear equations describing the resonant interaction of three waves in 1+1 dimensions. We display explicit solutions featuring localized waves whose profile vanishes at the spacial boundary |x|=∞, and which are not pure soliton solutions. These solutions depend on an arbitrary function and allow us to deal with collisions of waves with various profiles. © 2006 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)157-168
JournalPhysica D. Nonlinear Phenomena
Issue number2
Publication statusPublished - 2006

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