Abstract
A computational classification of contact symmetries and higher-order local symmetries that do not commute with , as well as local conserved densities that are not invariant under is carried out for a generalized version of the Krichever–Novikov (KN) equation. Several new results are obtained. First, the KN equation is explicitly shown to have a local conserved density that contains . Second, apart from the dilational point symmetries known for special cases of the KN equation and its generalized version, no other local symmetries with low differential order are found to contain . Third, the basic Hamiltonian structure of the KN equation is used to map the local conserved density containing into a nonlocal symmetry that contains . Fourth, a recursion operator is applied to this nonlocal symmetry to produce a hierarchy of nonlocal symmetries that have explicit dependence on . When the inverse of the Hamiltonian map is applied to this hierarchy, only trivial conserved densities are obtained.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Journal of Physics A: Mathematical and Theoretical
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.