Traveling waves for a nonlinear Schrödinger system with quadratic interaction
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917935990177792 |
|---|---|
| author | Fukaya, Noriyoshi Hayashi, Masayuki Inui, Takahisa |
| author_facet | Fukaya, Noriyoshi Hayashi, Masayuki Inui, Takahisa |
| contents | We study traveling wave solutions for a nonlinear Schrödinger system with quadratic interaction. For the non mass resonance case, the system has no Galilean symmetry, which is of particular interest in this paper. We construct traveling wave solutions by variational methods and see that for the non mass resonance case there exist specific traveling wave solutions which correspond to the solutions for ``zero mass" case in nonlinear elliptic equations. We also establish the new global existence result for oscillating data as an application. Both of our results essentially come from the lack of Galilean invariance in the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_05305 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Traveling waves for a nonlinear Schrödinger system with quadratic interaction Fukaya, Noriyoshi Hayashi, Masayuki Inui, Takahisa Analysis of PDEs We study traveling wave solutions for a nonlinear Schrödinger system with quadratic interaction. For the non mass resonance case, the system has no Galilean symmetry, which is of particular interest in this paper. We construct traveling wave solutions by variational methods and see that for the non mass resonance case there exist specific traveling wave solutions which correspond to the solutions for ``zero mass" case in nonlinear elliptic equations. We also establish the new global existence result for oscillating data as an application. Both of our results essentially come from the lack of Galilean invariance in the system. |
| title | Traveling waves for a nonlinear Schrödinger system with quadratic interaction |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2209.05305 |