Conservation of resonant periodic solutions for the one-dimensional nonlinear Schroedinger equation
Dynamical Systems
2015-06-26 v1 Analysis of PDEs
Abstract
We consider the one-dimensional nonlinear Schr\"odinger equation with Dirichlet boundary conditions in the fully resonant case (absence of the zero-mass term). We investigate conservation of small amplitude periodic-solutions for a large set measure of frequencies. In particular we show that there are infinitely many periodic solutions which continue the linear ones involving an arbitrary number of resonant modes, provided the corresponding frequencies are large enough and close enough to each other (wave packets with large wave number).
Keywords
Cite
@article{arxiv.math/0408017,
title = {Conservation of resonant periodic solutions for the one-dimensional nonlinear Schroedinger equation},
author = {Guido Gentile and Michela Procesi},
journal= {arXiv preprint arXiv:math/0408017},
year = {2015}
}