Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.05097 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929377388789760 |
|---|---|
| author | Yang, Su Chen, Shaoxuan Zhu, Wei Kevrekidis, P. G. |
| author_facet | Yang, Su Chen, Shaoxuan Zhu, Wei Kevrekidis, P. G. |
| contents | The moment quantities associated with the nonlinear Schrodinger equation offer important insights towards the evolution dynamics of such dispersive wave partial differential equation (PDE) models. The effective dynamics of the moment quantities is amenable to both analytical and numerical treatments. In this paper we present a data-driven approach associated with the Sparse Identification of Nonlinear Dynamics (SINDy) to numerically capture the evolution behaviors of such moment quantities. Our method is applied first to some well-known closed systems of ordinary differential equations (ODEs) which describe the evolution dynamics of relevant moment quantities. Our examples are, progressively, of increasing complexity and our findings explore different choices within the SINDy library. We also consider the potential discovery of coordinate transformations that lead to moment system closure. Finally, we extend considerations to settings where a closed analytical form of the moment dynamics is not available. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05097 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Identification of moment equations via data-driven approaches in nonlinear schrodinger models Yang, Su Chen, Shaoxuan Zhu, Wei Kevrekidis, P. G. Pattern Formation and Solitons Mathematical Physics The moment quantities associated with the nonlinear Schrodinger equation offer important insights towards the evolution dynamics of such dispersive wave partial differential equation (PDE) models. The effective dynamics of the moment quantities is amenable to both analytical and numerical treatments. In this paper we present a data-driven approach associated with the Sparse Identification of Nonlinear Dynamics (SINDy) to numerically capture the evolution behaviors of such moment quantities. Our method is applied first to some well-known closed systems of ordinary differential equations (ODEs) which describe the evolution dynamics of relevant moment quantities. Our examples are, progressively, of increasing complexity and our findings explore different choices within the SINDy library. We also consider the potential discovery of coordinate transformations that lead to moment system closure. Finally, we extend considerations to settings where a closed analytical form of the moment dynamics is not available. |
| title | Identification of moment equations via data-driven approaches in nonlinear schrodinger models |
| topic | Pattern Formation and Solitons Mathematical Physics |
| url | https://arxiv.org/abs/2406.05097 |