NLS approximation and dark solitons for the Adlam-Allen model of cold collisionless plasmas
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908332813451264 |
|---|---|
| author | Veldes, George P. Koukouloyannis, Vassilis Frantzeskakis, Dimitrios J. Kevrekidis, Panayotis G. |
| author_facet | Veldes, George P. Koukouloyannis, Vassilis Frantzeskakis, Dimitrios J. Kevrekidis, Panayotis G. |
| contents | The present work extends earlier considerations on a quintessential model of cold, collisionless plasmas, namely the Adlam-Allen model. Previously, an analysis of homoclinic solutions around a non-vanishing background (associated with a saddle equilibrium) led to a Korteweg-de Vries reduction. Here, we consider a different equilibrium of the co-traveling frame model, namely a center, and expanding around it, by means of a multiple-scale methodology and suitable scalings, leads to an effective defocusing nonlinear Schr{ö}dinger equation. Leveraging the latter, we construct, for the first time to our knowledge, physically realistic dark soliton waveforms of the Adlam-Allen model. We subsequently test the numerical evolution of such coherent structures, identifying them as long-lived waveforms of the full model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04707 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | NLS approximation and dark solitons for the Adlam-Allen model of cold collisionless plasmas Veldes, George P. Koukouloyannis, Vassilis Frantzeskakis, Dimitrios J. Kevrekidis, Panayotis G. Pattern Formation and Solitons The present work extends earlier considerations on a quintessential model of cold, collisionless plasmas, namely the Adlam-Allen model. Previously, an analysis of homoclinic solutions around a non-vanishing background (associated with a saddle equilibrium) led to a Korteweg-de Vries reduction. Here, we consider a different equilibrium of the co-traveling frame model, namely a center, and expanding around it, by means of a multiple-scale methodology and suitable scalings, leads to an effective defocusing nonlinear Schr{ö}dinger equation. Leveraging the latter, we construct, for the first time to our knowledge, physically realistic dark soliton waveforms of the Adlam-Allen model. We subsequently test the numerical evolution of such coherent structures, identifying them as long-lived waveforms of the full model. |
| title | NLS approximation and dark solitons for the Adlam-Allen model of cold collisionless plasmas |
| topic | Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2502.04707 |