Two soliton collision for nonlinear Schrödinger equations in dimension 1
Résumé
We study the collision of two solitons for the nonlinear Schrodinger equation i psi(t) = -psi(xx) + F(vertical bar psi vertical bar(2))psi, F(xi) = 2 xi + O(xi(2)) as xi --> 0, in the case where one soliton is small with respect to the other. We show that in general, the two soliton structure is not preserved after the collision: while the large soliton survives, the small one splits into two outgoing waves that for sufficiently long times can be controlled by the cubic NLS: i psi(t) = -psi(xx) -2 vertical bar psi vertical bar(2)psi.