Nonlinear stability of Gardner breathers
Analysis of PDEs
2017-09-26 v3
Abstract
We show that breather solutions of the Gardner equation, a natural generalization of the KdV and mKdV equations, are stable. Through a variational approach, we characterize Gardner breathers as minimizers of a new Lyapunov functional and we study the associated spectral problem, through the analysis of the spectrum of explicit linear systems (\emph{spectral stability}), and controlling degenerated directions by using low regularity conservation laws.
Cite
@article{arxiv.1705.04206,
title = {Nonlinear stability of Gardner breathers},
author = {Miguel A. Alejo},
journal= {arXiv preprint arXiv:1705.04206},
year = {2017}
}
Comments
This is v2. Improved with a complete stability result on the existence interval of the parameter $\mu\in(0,\mu_{max})$. 29 pages. arXiv admin note: text overlap with arXiv:1206.3157