Jakub Vašiček: 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 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.