Asymptotic Stability for KdV Solitons in Weighted $H^s$ Spaces
Analysis of PDEs
2014-10-28 v1
Abstract
In this work, we consider the stability of solitons for the KdV equation below the energy space, using spatially-exponentially-weighted norms. Using a combination of the -method and spectral analysis following Pego and Weinstein, we are able to show that, in the exponentially weighted space, the perturbation of a soliton decays exponentially for arbitrarily long times. The finite time restriction is due to a lack of global control of the unweighted perturbation.
Cite
@article{arxiv.1410.6873,
title = {Asymptotic Stability for KdV Solitons in Weighted $H^s$ Spaces},
author = {Brian Pigott and Sarah Raynor},
journal= {arXiv preprint arXiv:1410.6873},
year = {2014}
}