On the inelastic 2-soliton collision for gKdV equations with general nonlinearity
Analysis of PDEs
2012-03-01 v3 Mathematical Physics
math.MP
Abstract
We study the problem of 2-soliton collision for the generalized Korteweg-de Vries equations, completing some recent works of Y. Martel and F. Merle. We classify the nonlinearities for which collisions are elastic or inelastic. Our main result states that in the case of small solitons, with one soliton smaller than the other one, the unique nonlinearities allowing a perfectly elastic collision are precisely the integrable cases, namely the quadratic (KdV), cubic (mKdV) and Gardner nonlinearities.
Keywords
Cite
@article{arxiv.0903.1240,
title = {On the inelastic 2-soliton collision for gKdV equations with general nonlinearity},
author = {Claudio Muñoz},
journal= {arXiv preprint arXiv:0903.1240},
year = {2012}
}
Comments
54 pages, submitted; corrected a gap in a previous computation