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arXiv · 2305.03858

The stability of degenerate solitons for derivative nonlinear Schrodinger equations

Taegyu Kim
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Abstract

In this paper, we consider the following nonlinear Schr\"odinger equation with derivative: \begin{align*} i\partial_tu+\partial_{xx}u+i|u|^{2}\partial_xu+b|u|^4u=0, \quad (t,x) \in \mathbb{R}\times\mathbb{R}, \quad b\geq 0. \end{align*} For the case $b=0$, the original DNLS, Kwon and Wu \cite{KwonWu2018} proved the conditional orbital stability of degenerate solitons including scaling, phase rotation, and spatial translation with a non-smallness condition, $\|u(t)\|_{L^6}^6> \sqrt{\delta}$. In this paper, we remove this condition for the non-positive initial energy and momentum, and we extend the stability result for $b\geq0$.

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Taegyu Kim. 2023-05-05. The stability of degenerate solitons for derivative nonlinear Schrodinger equations. https://doi.org/10.1016/j.jmaa.2024.128524

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