Global solutions to nonconservative NLS with non-decaying initial data

Le résumé fourni par la source

We investigate the long-time behavior of solutions to nonconservative nonlinear Schrödinger equations (NLS) of the form i ∂ t u = − ∂ x 2 u − u p , p ∈ N , p ≥ 2 . We focus on initial data that are neither localized nor periodic. Our approach is based on the work [13] by Jaquette, Lessard and Takayasu, where they used a perturbative analysis around the explicit spatially homogeneous solution of the associated ODE. Using their methods, we establish global existence results and asymptotic decay of solutions in a general Banach algebra setting. Applications include small data global well-posedness results for almost periodic initial data, which seem to be the first in a nonconservative NLS framework. Applications to (almost) periodic initial data with localized perturbations are also presented.

Ce résumé expose les affirmations des auteurs. BNTIC ne l’interprète pas comme une validation indépendante des résultats.