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Dispersive Hydrodynamics of Soliton Condensates for the Korteweg–de Vries Equation
We consider large-scale dynamics of non-equilibrium dense soliton gas for the Korteweg–de Vries (KdV) equation in the special “condensate” limit. We prove that in this limit the integro-differential kinetic equation for the spectral density of states reduces to the N-phase KdV–Whitham modulation equ...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer US
2023
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10509137/ https://www.ncbi.nlm.nih.gov/pubmed/37736286 http://dx.doi.org/10.1007/s00332-023-09940-y |
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author | Congy, T. El, G. A. Roberti, G. Tovbis, A. |
author_facet | Congy, T. El, G. A. Roberti, G. Tovbis, A. |
author_sort | Congy, T. |
collection | PubMed |
description | We consider large-scale dynamics of non-equilibrium dense soliton gas for the Korteweg–de Vries (KdV) equation in the special “condensate” limit. We prove that in this limit the integro-differential kinetic equation for the spectral density of states reduces to the N-phase KdV–Whitham modulation equations derived by Flaschka et al. (Commun Pure Appl Math 33(6):739–784, 1980) and Lax and Levermore (Commun Pure Appl Math 36(5):571–593, 1983). We consider Riemann problems for soliton condensates and construct explicit solutions of the kinetic equation describing generalized rarefaction and dispersive shock waves. We then present numerical results for “diluted” soliton condensates exhibiting rich incoherent behaviors associated with integrable turbulence. |
format | Online Article Text |
id | pubmed-10509137 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | Springer US |
record_format | MEDLINE/PubMed |
spelling | pubmed-105091372023-09-21 Dispersive Hydrodynamics of Soliton Condensates for the Korteweg–de Vries Equation Congy, T. El, G. A. Roberti, G. Tovbis, A. J Nonlinear Sci Article We consider large-scale dynamics of non-equilibrium dense soliton gas for the Korteweg–de Vries (KdV) equation in the special “condensate” limit. We prove that in this limit the integro-differential kinetic equation for the spectral density of states reduces to the N-phase KdV–Whitham modulation equations derived by Flaschka et al. (Commun Pure Appl Math 33(6):739–784, 1980) and Lax and Levermore (Commun Pure Appl Math 36(5):571–593, 1983). We consider Riemann problems for soliton condensates and construct explicit solutions of the kinetic equation describing generalized rarefaction and dispersive shock waves. We then present numerical results for “diluted” soliton condensates exhibiting rich incoherent behaviors associated with integrable turbulence. Springer US 2023-09-19 2023 /pmc/articles/PMC10509137/ /pubmed/37736286 http://dx.doi.org/10.1007/s00332-023-09940-y Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Article Congy, T. El, G. A. Roberti, G. Tovbis, A. Dispersive Hydrodynamics of Soliton Condensates for the Korteweg–de Vries Equation |
title | Dispersive Hydrodynamics of Soliton Condensates for the Korteweg–de Vries Equation |
title_full | Dispersive Hydrodynamics of Soliton Condensates for the Korteweg–de Vries Equation |
title_fullStr | Dispersive Hydrodynamics of Soliton Condensates for the Korteweg–de Vries Equation |
title_full_unstemmed | Dispersive Hydrodynamics of Soliton Condensates for the Korteweg–de Vries Equation |
title_short | Dispersive Hydrodynamics of Soliton Condensates for the Korteweg–de Vries Equation |
title_sort | dispersive hydrodynamics of soliton condensates for the korteweg–de vries equation |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10509137/ https://www.ncbi.nlm.nih.gov/pubmed/37736286 http://dx.doi.org/10.1007/s00332-023-09940-y |
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