Nonlocal Symmetries of the Camassa-Holm Type Equations
| Autor: | Changzheng Qu, Lu Zhao |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Class (set theory) Recursion operator Applied Mathematics General Mathematics 010102 general mathematics Mathematics::Analysis of PDEs Inverse Type (model theory) 01 natural sciences 010104 statistics & probability Nonlinear Sciences::Exactly Solvable and Integrable Systems Factorization Homogeneous space Novikov self-consistency principle 0101 mathematics Korteweg–de Vries equation Nonlinear Sciences::Pattern Formation and Solitons Mathematics |
| Zdroj: | Chinese Annals of Mathematics, Series B. 41:407-418 |
| ISSN: | 1860-6261 0252-9599 |
| DOI: | 10.1007/s11401-020-0207-8 |
| Popis: | A class of nonlocal symmetries of the Camassa-Holm type equations with bi-Hamiltonian structures, including the Camassa-Holm equation, the modified Camassa-Holm equation, Novikov equation and Degasperis-Procesi equation, is studied. The nonlocal symmetries are derived by looking for the kernels of the recursion operators and their inverse operators of these equations. To find the kernels of the recursion operators, the authors adapt the known factorization results for the recursion operators of the KdV, modified KdV, Sawada-Kotera and Kaup-Kupershmidt hierarchies, and the explicit Liouville correspondences between the KdV and Camassa-Holm hierarchies, the modified KdV and modified Camassa-Holm hierarchies, the Novikov and Sawada-Kotera hierarchies, as well as the Degasperis-Procesi and Kaup-Kupershmidt hierarchies. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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