Validity of the nonlinear Schr\"odinger approximation for quasilinear dispersive systems with more than one derivative
Abstract
For nonlinear dispersive systems, the nonlinear Schr\"odinger (NLS) equation can usually be derived as a formal approximation equation describing slow spatial and temporal modulations of the envelope of a spatially and temporally oscillating underlying carrier wave. Here, we justify the NLS approximation for a whole class of quasilinear dispersive systems, which also includes toy models for the waterwave problem. This is the first time that this is done for systems, where a quasilinear quadratic term is allowed to effectively lose more than one derivative. With effective loss we here mean the loss still present after making a diagonalization of the linear part of the system such that all linear operators in this diagonalization have the same regularity properties.
Keywords
Cite
@article{arxiv.2005.02051,
title = {Validity of the nonlinear Schr\"odinger approximation for quasilinear dispersive systems with more than one derivative},
author = {Max Heß},
journal= {arXiv preprint arXiv:2005.02051},
year = {2021}
}