Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.01919 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911121247567872 |
|---|---|
| author | Li, Yuan |
| author_facet | Li, Yuan |
| contents | In this paper, we consider the subcritical half-wave equation in one dimension. Let $R_k(t,x)$, $k=1,2$, represent two-solitary wave solutions of the half-wave equation, each with different translations $x_1,x_2$. We prove that if the relative distance $x_2-x_1$ between the two solitary waves is large enough, then the sum of $R_k(t)$ is weakly stable. Our proof relies on an energy method and the local mass monotonicity property. Unlike the single-solitary wave or NLS cases, the interactions between different waves are significantly stronger here. To establish the local mass monotonicity property, as well as to analyze non-local effects on localization functions and non-local operator $D$, we utilize the Carlderón estimate and the integral representation formula of the half-wave operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01919 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weak stability of the sum of two solitary waves for Half-wave equation Li, Yuan Analysis of PDEs In this paper, we consider the subcritical half-wave equation in one dimension. Let $R_k(t,x)$, $k=1,2$, represent two-solitary wave solutions of the half-wave equation, each with different translations $x_1,x_2$. We prove that if the relative distance $x_2-x_1$ between the two solitary waves is large enough, then the sum of $R_k(t)$ is weakly stable. Our proof relies on an energy method and the local mass monotonicity property. Unlike the single-solitary wave or NLS cases, the interactions between different waves are significantly stronger here. To establish the local mass monotonicity property, as well as to analyze non-local effects on localization functions and non-local operator $D$, we utilize the Carlderón estimate and the integral representation formula of the half-wave operator. |
| title | Weak stability of the sum of two solitary waves for Half-wave equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.01919 |