Geometric singular perturbation analysis to Camassa-Holm Kuramoto-Sivashinsky equation
| Autor: | Zengji Du, Ji Li |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
Singular perturbation
Applied Mathematics Perturbation (astronomy) Kuramoto–Sivashinsky equation Observable Wave speed Nonlinear Sciences::Exactly Solvable and Integrable Systems Singular perturbation analysis Slow manifold Soliton Nonlinear Sciences::Pattern Formation and Solitons Analysis Mathematics Mathematical physics |
| Zdroj: | Journal of Differential Equations. 306:418-438 |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2021.10.033 |
| Popis: | We analyze a singularly Kuramoto-Sivashinsky perturbed Camassa-Holm equation with methods of the geometric singular perturbation theory. Especially, we study the persistence of smooth and peaked solitons. Whether a solitary wave of the original Camassa-Holm equation is smooth or peaked depends on whether there is linear dispersion, i.e. whether 2 k = 0 . If 2 k > 0 , then a unique smooth solitary wave persists with selected wave speed under singular Kuramoto-Sivashinsky perturbation just as what happens in the KS-KdV equation. On the other hand, we show that if there is no linear dispersion, i.e. 2 k = 0 , then any observable peaked soliton fails to persist. This case is non-typical since the related slow manifold blows up and the classical geometric singular perturbation theory is not available. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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