Space Curves from Nonlinear Schrödinger Solutions: A Direct Approach
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2019
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866929264814718976 |
|---|---|
| author | Abhinav, Kumar Guha, Partha |
| author_facet | Abhinav, Kumar Guha, Partha |
| contents | The connection between vortex filament evolution in the local induction approximation and non-linear Schrödinger (NLS) equation by Hasimoto [H. Hasimoto, J. Fluid Mechanics 51, (1972) 477] has led to space curves corresponding to NLS solitons in the past. Utilizing this map, we propose a direct construction of parametric curve evolution from any NLS solution. It includes ordered (or nested) integrals of products of local matrices akin to the causal evolution of quantum theory, necessitating the implementation of the Magnus expansion. Such a straightforward mapping may be a simple tool to study the evolution of various systems of physical concern, although the actual computation can be a challenge for most NLS solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1905_06659 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Space Curves from Nonlinear Schrödinger Solutions: A Direct Approach Abhinav, Kumar Guha, Partha Exactly Solvable and Integrable Systems Mathematical Physics The connection between vortex filament evolution in the local induction approximation and non-linear Schrödinger (NLS) equation by Hasimoto [H. Hasimoto, J. Fluid Mechanics 51, (1972) 477] has led to space curves corresponding to NLS solitons in the past. Utilizing this map, we propose a direct construction of parametric curve evolution from any NLS solution. It includes ordered (or nested) integrals of products of local matrices akin to the causal evolution of quantum theory, necessitating the implementation of the Magnus expansion. Such a straightforward mapping may be a simple tool to study the evolution of various systems of physical concern, although the actual computation can be a challenge for most NLS solutions. |
| title | Space Curves from Nonlinear Schrödinger Solutions: A Direct Approach |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics |
| url | https://arxiv.org/abs/1905.06659 |