On the inelastic 2-soliton collision for gKdV equations with general nonlinearity

Details On the inelastic 2-soliton collision for gKdV equations with general nonlinearity On the inelastic 2-soliton collision for gKdV equations with general nonlinearity

2009-03-06

arxiv.org/abs/0903.1240v3

Int. Math. Res. Notices (2010) 2010 (9): 1624-1719

Mathematics

Analysis of PDEs

54 pages, submitted; corrected a gap in a previous computation

Scientific paper

10.1093/imrn/rnp204

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.

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