Gain of regularity for a coupled system of generalized nonlinear Schrödinger equations
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911879853506560 |
|---|---|
| author | Mollisaca, Raul Nina Cortés, Mauricio Sepúlveda Asem, Rodrigo Véjar Villagrán, Octavio Vera |
| author_facet | Mollisaca, Raul Nina Cortés, Mauricio Sepúlveda Asem, Rodrigo Véjar Villagrán, Octavio Vera |
| contents | In this paper we study the smoothness properties of solutions to a one-dimensional coupled nonlinear Schrödinger system equations that describes some physical phenomena such as propagation of polarized laser beams in birefringent Kerr medium in nonlinear optics. We show that the equations dispersive nature leads to a gain in regularity for the solution. In particular, if the initial data $(u_{0},\,v_{0})$ possesses certain regularity and sufficient decay as $|x|\rightarrow\infty,$ then the solution $(u(t),\,v(t))$ will be smoother than $(u_{0},\,v_{0})$ for $0 < t \leq T$ where $T$ is the existence time of the solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_07816 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gain of regularity for a coupled system of generalized nonlinear Schrödinger equations Mollisaca, Raul Nina Cortés, Mauricio Sepúlveda Asem, Rodrigo Véjar Villagrán, Octavio Vera Analysis of PDEs 35Q53 (Primary), 47J353 (Secondary) In this paper we study the smoothness properties of solutions to a one-dimensional coupled nonlinear Schrödinger system equations that describes some physical phenomena such as propagation of polarized laser beams in birefringent Kerr medium in nonlinear optics. We show that the equations dispersive nature leads to a gain in regularity for the solution. In particular, if the initial data $(u_{0},\,v_{0})$ possesses certain regularity and sufficient decay as $|x|\rightarrow\infty,$ then the solution $(u(t),\,v(t))$ will be smoother than $(u_{0},\,v_{0})$ for $0 < t \leq T$ where $T$ is the existence time of the solution. |
| title | Gain of regularity for a coupled system of generalized nonlinear Schrödinger equations |
| topic | Analysis of PDEs 35Q53 (Primary), 47J353 (Secondary) |
| url | https://arxiv.org/abs/2301.07816 |