On the Whitham modulation equations for the Toda lattice and the quantitative characterization of its dispersive shocks
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917831967244288 |
|---|---|
| author | Biondini, Gino Chong, Christopher Kevrekidis, Panayotis |
| author_facet | Biondini, Gino Chong, Christopher Kevrekidis, Panayotis |
| contents | The aim of this work is multifold. Firstly, it intends to present a complete, quantitative and self-contained description of the periodic traveling wave solutions and Whitham modulation equations for the Toda lattice, combining results from different previous works in the literature. Specifically, we connect the Whitham modulation equations and a detailed expression for the periodic traveling wave solutions of the Toda lattice. Along the way, some key details are filled in, such as the explicit expression of the characteristic speeds of the genus-one Toda-Whitham system. Secondly, we use these tools to obtain a detailed quantitative characterization of the dispersive shocks of the Toda system. Lastly, we validate the relevant analysis by performing a detailed comparison with direct numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_10755 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Whitham modulation equations for the Toda lattice and the quantitative characterization of its dispersive shocks Biondini, Gino Chong, Christopher Kevrekidis, Panayotis Exactly Solvable and Integrable Systems Pattern Formation and Solitons The aim of this work is multifold. Firstly, it intends to present a complete, quantitative and self-contained description of the periodic traveling wave solutions and Whitham modulation equations for the Toda lattice, combining results from different previous works in the literature. Specifically, we connect the Whitham modulation equations and a detailed expression for the periodic traveling wave solutions of the Toda lattice. Along the way, some key details are filled in, such as the explicit expression of the characteristic speeds of the genus-one Toda-Whitham system. Secondly, we use these tools to obtain a detailed quantitative characterization of the dispersive shocks of the Toda system. Lastly, we validate the relevant analysis by performing a detailed comparison with direct numerical simulations. |
| title | On the Whitham modulation equations for the Toda lattice and the quantitative characterization of its dispersive shocks |
| topic | Exactly Solvable and Integrable Systems Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2312.10755 |