Affiliation:
1. School of Mathematics and Statistics, Ningbo University , Ningbo 315211, People’s Republic of China
Abstract
In this paper, we consider the connection between generalized conditional symmetries (GCSs) and pre-Hamiltonian operators. The set of GCSs of an evolutionary partial differential equations system is divided into a union of many linear subspaces by different characteristic operators, and we consider the mappings between two of them, which generalize the recursion operators of symmetries and the pre-Hamiltonian operators. Finally, we give a systematic method to construct infinitely many GCSs for integrable systems, including the Gelfand–Dickey hierarchy and the AKNS-D hierarchy. All time flows in one integrable hierarchy, admitting infinitely many common GCSs.
Funder
National Natural Science Foundation of China
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Reference23 articles.
1. Exactly integrable hyperbolic equations of Liouville type;Russ. Math. Surv.,2001
2. On a family of operators and their Lie algebras;J. Lie Theory,2002
3. Involutive distributions of operator-valued evolutionary vector fields and their affine geometry,2011
4. A sufficient condition for a rational differential operator to generate an integrable system;Jpn. J. Math.,2017
5. PreHamiltonian and Hamiltonian operators for differential-difference equations;Nonlinearity,2020