Symmetries and conservation laws of the generalized Krichever–Novikov equation
| Autor: | Stephen C. Anco, L. R. Galiakberova, A. A. Gainetdinova, Thomas Wolf, Elena D. Avdonina, Nail H. Ibragimov |
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| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
Recursion operator FOS: Physical sciences General Physics and Astronomy Inverse 01 natural sciences symbols.namesake Hamiltonian structure 0101 mathematics Mathematical Physics Mathematical physics Physics Conservation law Nonlinear Sciences - Exactly Solvable and Integrable Systems 010102 general mathematics Statistical and Nonlinear Physics Mathematical Physics (math-ph) Invariant (physics) 010101 applied mathematics Nonlinear Sciences::Exactly Solvable and Integrable Systems Modeling and Simulation Homogeneous space symbols Novikov self-consistency principle Exactly Solvable and Integrable Systems (nlin.SI) Hamiltonian (quantum mechanics) |
| Zdroj: | Journal of Physics A: Mathematical and Theoretical. 49:105201 |
| ISSN: | 1751-8121 1751-8113 |
| DOI: | 10.1088/1751-8113/49/10/105201 |
| Popis: | A computational classification of contact symmetries and higher-order local symmetries that do not commute with $t,x$, as well as local conserved densities that are not invariant under $t,x$ is carried out for a generalized version of the Krichever-Novikov equation. Several new results are obtained. First, the Krichever-Novikov equation is explicitly shown to have a local conserved density that contains $t,x$. Second, apart from the dilational point symmetries known for special cases of the Krichever-Novikov equation and its generalized version, no other local symmetries with low differential order are found to contain $t,x$. Third, the basic Hamiltonian structure of the Krichever-Novikov equation is used to map the local conserved density containing $t,x$ into a nonlocal symmetry that contains $t,x$. Fourth, a recursion operator is applied to this nonlocal symmetry to produce a hierarchy of nonlocal symmetries that have explicit dependence on $t,x$. When the inverse of the Hamiltonian map is applied to this hierarchy, only trivial conserved densities are obtained. 27 pages; published version |
| Databáze: | OpenAIRE |
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