General rogue waves of infinite order: Exact properties, asymptotic behavior, and effective numerical computation
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914908905406464 |
|---|---|
| author | Bilman, Deniz Miller, Peter D. |
| author_facet | Bilman, Deniz Miller, Peter D. |
| contents | This paper is devoted to a comprehensive analysis of a family of solutions of the focusing nonlinear Schrödinger equation called general rogue waves of infinite order. These solutions have recently been shown to describe various limit processes involving large-amplitude waves, and they have also appeared in some physical models not directly connected with nonlinear Schrödinger equations. We establish the following key property of these solutions: they are all in $L^2(\mathbb{R})$ with respect to the spatial variable but they exhibit anomalously slow temporal decay. In this paper we define general rogue waves of infinite order, establish their basic exact and asymptotic properties, and provide computational tools for calculating them accurately. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05390 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | General rogue waves of infinite order: Exact properties, asymptotic behavior, and effective numerical computation Bilman, Deniz Miller, Peter D. Analysis of PDEs Mathematical Physics Exactly Solvable and Integrable Systems 35Q55, 35Q15, 35Q51, 37K10, 37K15, 37K40, 34M55 This paper is devoted to a comprehensive analysis of a family of solutions of the focusing nonlinear Schrödinger equation called general rogue waves of infinite order. These solutions have recently been shown to describe various limit processes involving large-amplitude waves, and they have also appeared in some physical models not directly connected with nonlinear Schrödinger equations. We establish the following key property of these solutions: they are all in $L^2(\mathbb{R})$ with respect to the spatial variable but they exhibit anomalously slow temporal decay. In this paper we define general rogue waves of infinite order, establish their basic exact and asymptotic properties, and provide computational tools for calculating them accurately. |
| title | General rogue waves of infinite order: Exact properties, asymptotic behavior, and effective numerical computation |
| topic | Analysis of PDEs Mathematical Physics Exactly Solvable and Integrable Systems 35Q55, 35Q15, 35Q51, 37K10, 37K15, 37K40, 34M55 |
| url | https://arxiv.org/abs/2408.05390 |