Exact solutions of the 3-wave resonant interaction equation

Antonio Degasperis, Sara Lombardo

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)157-168
JournalPhysica D: Nonlinear Phenomena
Issue number2
Publication statusPublished - Feb 2006


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