Abstract
Starting from 10 sets of symmetries of the Kawamoto equation, one can get 10 hierarchies of corresponding integrable models. These hierarchies possess the same recursion operator but they do not possess common symmetry structure. Only two hierarchies related to the kernel of inverse recursion operators have the same time-independent symmetry structure as that of the Kawamoto equation. However, the symmetry algebras of the other eight hierarchies are only isomorphic to some subalgebras of that of the Kawamoto equation. Especially, three hierarchies of them possess six sets of time-independent noncommute symmetries while the other five hierarchies possess only four sets of time-independent but commute symmetries. Only one set of time-dependent symmetries for all ten hierarchies is obtained. Using the point symmetry algebra of the Kawamoto equation, various new complex group-invariant solutions (similarity reductions) of the Kawamoto equation are also given.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
