Exact solutions of the 3-wave resonant interaction equation

Antonio Degasperis, Sara Lombardo*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)

Abstract

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
Number of pages12
JournalPhysica D: Nonlinear Phenomena
Volume214
Issue number2
DOIs
Publication statusPublished - 15 Feb 2006

Keywords

  • 3-wave interaction
  • Integrable PDEs
  • Solitons

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Exact solutions of the 3-wave resonant interaction equation'. Together they form a unique fingerprint.

Cite this