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 language | English |
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Pages (from-to) | 157-168 |
Number of pages | 12 |
Journal | Physica D: Nonlinear Phenomena |
Volume | 214 |
Issue number | 2 |
DOIs | |
Publication status | Published - 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