Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data

Liu, Jiaqi; Perry, Peter A.; Sulem, Catherine

Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 1, pp. 217-265.

On établit le comportement au temps long des solutions de l'équation de Schrödinger nonlinéraire avec dérivée dans des espaces de Sobolev à poids, sous l'hypothèse que les conditions initiales ne supportent pas de solitons. Notre approche utilise l'inverse scattering et la méthode de la plus grande pente (“steepest descent”) nonlinéaire de Deift et Zhou revisitée par Dieng et McLaughlin.

The large-time behavior of solutions to the derivative nonlinear Schrödinger equation is established for initial conditions in some weighted Sobolev spaces under the assumption that the initial conditions do not support solitons. Our approach uses the inverse scattering setting and the nonlinear steepest descent method of Deift and Zhou as recast by Dieng and McLaughlin.

Mots clés : Riemann–Hilbert problem, Inverse scattering method, Nonlinear steepest descent method

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