Exact solutions of the 3-wave resonant interaction equation
Exactly Solvable and Integrable Systems
2015-06-26 v1 Mathematical Physics
math.MP
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 plus and minus infinity, and which are not pure soliton solutions. These solutions depend on an arbitrary function and allow to deal with collisions of waves with various profiles.
Keywords
Cite
@article{arxiv.nlin/0509038,
title = {Exact solutions of the 3-wave resonant interaction equation},
author = {Antonio Degasperis and Sara Lombardo},
journal= {arXiv preprint arXiv:nlin/0509038},
year = {2015}
}
Comments
15 pages, 9 figures, standard LaTeX2e, submitted for publication to Physica D