Travelling wave solutions on a non-zero background for the generalized Korteweg-de Vries equation
| Autor: | Anco, Stephen C., Nayeri, HamidReza, Recio, Elena |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | J Phys A: Math. Theor. 54(7) (2021), 085701 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1751-8121/abda77 |
| Popis: | For the generalized $p$-power Korteweg-de Vries equation, all non-periodic travelling wave solutions with non-zero boundary conditions are explicitly classified for all integer powers $p\geq 1$. These solutions are shown to consist of: bright solitary waves and static humps on a non-zero background for odd $p$; dark solitary waves on a non-zero background and kink waves for even $p$ in the defocusing case; pairs of bright/dark solitary waves on a non-zero background, and also bright and dark heavy-tail waves (with power decay) on a non-zero background, for even $p$ in the focusing case. An explicit physical parameterization is given for each type of solutionin terms of the wave speed $c$, background size $b$, and wave height/depth $h$. The allowed kinematic region in $(c,b)$ as well as in $(h,b)$ for existence of the solutions is derived, and other main kinematic features are discussed. Explicit formulas are presented in the integrable cases $p=1,2$, and in the higher power cases $p=3,4$. Comment: 47 pages; 24 figures; references added and sections re-organzed |
| Databáze: | arXiv |
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