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arXiv · 1705.04206

Nonlinear stability of Gardner breathers

Miguel A. Alejo
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Abstract

We show that breather solutions of the Gardner equation, a natural generalization of the KdV and mKdV equations, are $H^2(\mathbb{R})$ stable. Through a variational approach, we characterize Gardner breathers as minimizers of a new Lyapunov functional and we study the associated spectral problem, through $(i)$ the analysis of the spectrum of explicit linear systems (\emph{spectral stability}), and $(ii)$ controlling degenerated directions by using low regularity conservation laws.

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Miguel A. Alejo. 2017-05-10. Nonlinear stability of Gardner breathers. https://arxiv.org/abs/1705.04206

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