Rational solitons of wave resonant interaction models
Abstract
Integrable models of resonant interaction of two or more waves in 1+1 dimensions are known to be of applicative interest in several areas. Here we consider a system of three coupled wave equations which includes as special cases the vector Nonlinear Schroedinger equations and the equations describing the resonant interaction of three waves. The Darboux-Dressing construction of soliton solutions is applied under the condition that the solutions have rational, or mixed rational-exponential, dependence on coordinates. Our algebraic construction relies on the use of nilpotent matrices and their Jordan form. We systematically search for all bounded rational (mixed rational-exponential) solutions and find, for the first time to our knowledge, a broad family of such solutions of the three wave resonant interaction equations.
Keywords
Cite
@article{arxiv.1305.6636,
title = {Rational solitons of wave resonant interaction models},
author = {Antonio Degasperis and Sara Lombardo},
journal= {arXiv preprint arXiv:1305.6636},
year = {2015}
}
Comments
28 pages, 35 figures, standard LaTeX2e