Symmetries and conservation laws for a generalization of Kawahara equation

We give a complete description of generalized and formal symmetries for a nonlinear evolution equation which generalizes the Kawahara equation having important applications in the study of plasma waves and capillary–gravity water waves. Using these results and the presence of Hamiltonian structure w...

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Bibliographic Details
Published in:Journal of geometry and physics 2020-04, Vol.150, p.103579, Article 103579
Main Author: Vašíček, Jakub
Format: Article
Language:English
Subjects:
Conservation laws
Formal symmetries
Hamiltonian structures
Integrability
Symmetries
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Summary:We give a complete description of generalized and formal symmetries for a nonlinear evolution equation which generalizes the Kawahara equation having important applications in the study of plasma waves and capillary–gravity water waves. Using these results and the presence of Hamiltonian structure we also give a complete description of local conservation laws for the equation under study. In particular, we show that the equation in question admits no genuinely generalized symmetries and has only finitely many nontrivial linearly independent local conservation laws, and thus this equation is not symmetry integrable.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2019.103579