The stability of degenerate solitons for derivative nonlinear Schrodinger equations
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917532446752768 |
|---|---|
| author | Kim, Taegyu |
| author_facet | Kim, Taegyu |
| contents | In this paper, we consider the following nonlinear Schrödinger 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, $\|u(t)\|_{L^6}^6> \sqrtδ$. In this paper, we remove this condition for the non-positive initial energy and momentum, and we extend the stability result for $b\geq0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_03858 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The stability of degenerate solitons for derivative nonlinear Schrodinger equations Kim, Taegyu Analysis of PDEs In this paper, we consider the following nonlinear Schrödinger 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, $\|u(t)\|_{L^6}^6> \sqrtδ$. In this paper, we remove this condition for the non-positive initial energy and momentum, and we extend the stability result for $b\geq0$. |
| title | The stability of degenerate solitons for derivative nonlinear Schrodinger equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2305.03858 |