Modified Energy Functionals and the NLS Approximation
Analysis of PDEs
2016-06-02 v1
Abstract
We consider a model equation from [14] that captures important properties of the water wave equation. We give a new proof of the fact that wave packet solutions of this equation are approximated by the nonlinear Schrodinger equation. This proof both simplifies and strengthens the results of [14] so that the approximation holds for the full interval of existence of the approximate NLS solution rather than just a subinterval. Furthermore, the proof avoids the problems associated with inverting the normal form transform in [14] by working with a modified energy functional motivated by [1] and [8].
Cite
@article{arxiv.1606.00028,
title = {Modified Energy Functionals and the NLS Approximation},
author = {Patrick Cummings and C. Eugene Wayne},
journal= {arXiv preprint arXiv:1606.00028},
year = {2016}
}