On the Benjamin and Related Equations: On the Benjamin and Related Equations
We consider in this paper various theoretical and numerical issues on classical one dimensional models of internal waves with surface tension. They concern the Cauchy problem, including the long time dynamic, localized solitons or multisolitons, the soliton resolution property. We survey known resul...
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| Veröffentlicht in: | Boletim da Sociedade Brasileira de Matemática 2025-03, Vol.56 (1), Article 4 |
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| creator | Klein, Christian Linares, Felipe Pilod, Didier Saut, Jean-Claude |
| description | We consider in this paper various theoretical and numerical issues on classical one dimensional models of internal waves with surface tension. They concern the Cauchy problem, including the long time dynamic, localized solitons or multisolitons, the soliton resolution property. We survey known results, present a few new ones together with open questions and conjectures motivated by numerical simulations. A major issue is to emphasize the differences of the qualitative behavior of solutions with those of the same equations without the capillary term. |
| doi_str_mv | 10.1007/s00574-024-00428-1 |
| format | Article |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Capillary waves Cauchy problems Internal waves Mathematical and Computational Physics Mathematics Mathematics and Statistics One dimensional models Solitary waves Surface tension Theoretical |
| title | On the Benjamin and Related Equations: On the Benjamin and Related Equations |
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