Representations of sl(2,?) in category O and master symmetries

Wang, Jing Ping (2015) Representations of sl(2,?) in category O and master symmetries. Theoretical and Mathematical Physics, 184 (2). pp. 1078-1105. ISSN 0040-5779. (doi:https://doi.org/10.1007/s11232-015-0319-6) (Full text available)

Abstract

We show that the indecomposable sl(2,?)-modules in the Bernstein-Gelfand-Gelfand category O naturally arise for homogeneous integrable nonlinear evolution systems. We then develop a new approach called the O scheme to construct master symmetries for such integrable systems. This method naturally allows computing the hierarchy of time-dependent symmetries. We finally illustrate the method using both classical and new examples. We compare our approach to the known existing methods used to construct master symmetries. For new integrable equations such as a Benjamin-Ono-type equation, a new integrable Davey-Stewartson-type equation, and two different versions of (2+1)-dimensional generalized Volterra chains, we generate their conserved densities using their master symmetries.

Item Type:	Article
Uncontrolled keywords:	Homogeneous integrable nonlinear equations, the BGG category O, Master symmetries, Conservation laws, Symmetries.
Subjects:	Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Divisions:	Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User:	Jing Ping Wang
Date Deposited:	23 Sep 2015 15:40 UTC
Last Modified:	26 Jun 2017 17:30 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/50598 (The current URI for this page, for reference purposes)