Collapse dynamics for two-dimensional space-time nonlocal nonlinear Schrodinger equations
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914682596491264 |
|---|---|
| author | Cole, Justin T. Aurko, Abdullah M. Musslimani, Ziad H. |
| author_facet | Cole, Justin T. Aurko, Abdullah M. Musslimani, Ziad H. |
| contents | The question of collapse (blow-up) in finite time is investigated for the two-dimensional (non-integrable) space-time nonlocal nonlinear Schrodinger equations. Starting from the two-dimensional extension of the well known AKNS q,r system, three different cases are considered: (i) partial and full parity-time (PT) symmetric, (ii) reverse-time (RT) symmetric, and (iii) general q,r system. Through extensive numerical experiments, it is shown that collapse of Gaussian initial conditions depends on the value of its quasi-power. The collapse dynamics (or lack thereof) strongly depends on whether the nonlocality is in space or time. A so-called quasi-variance identity is derived and its relationship to blow-up is discussed. Numerical simulations reveal that this quantity reaching zero in finite time does not (in general) guarantee collapse. An alternative approach to the study of wave collapse is presented via the study of transverse instability of line soliton solutions. In particular, the linear stability problem for perturbed solitons is formulated for the nonlocal RT and PT symmetric nonlinear Schrodinger (NLS) equations. Through a combination of numerical and analytical approaches, the stability spectrum for some stationary one soliton solutions is found. Direct numerical simulations agree with the linear stability analysis which predicts filamentation and subsequent blow-up. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_04443 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Collapse dynamics for two-dimensional space-time nonlocal nonlinear Schrodinger equations Cole, Justin T. Aurko, Abdullah M. Musslimani, Ziad H. Pattern Formation and Solitons Analysis of PDEs The question of collapse (blow-up) in finite time is investigated for the two-dimensional (non-integrable) space-time nonlocal nonlinear Schrodinger equations. Starting from the two-dimensional extension of the well known AKNS q,r system, three different cases are considered: (i) partial and full parity-time (PT) symmetric, (ii) reverse-time (RT) symmetric, and (iii) general q,r system. Through extensive numerical experiments, it is shown that collapse of Gaussian initial conditions depends on the value of its quasi-power. The collapse dynamics (or lack thereof) strongly depends on whether the nonlocality is in space or time. A so-called quasi-variance identity is derived and its relationship to blow-up is discussed. Numerical simulations reveal that this quantity reaching zero in finite time does not (in general) guarantee collapse. An alternative approach to the study of wave collapse is presented via the study of transverse instability of line soliton solutions. In particular, the linear stability problem for perturbed solitons is formulated for the nonlocal RT and PT symmetric nonlinear Schrodinger (NLS) equations. Through a combination of numerical and analytical approaches, the stability spectrum for some stationary one soliton solutions is found. Direct numerical simulations agree with the linear stability analysis which predicts filamentation and subsequent blow-up. |
| title | Collapse dynamics for two-dimensional space-time nonlocal nonlinear Schrodinger equations |
| topic | Pattern Formation and Solitons Analysis of PDEs |
| url | https://arxiv.org/abs/2311.04443 |