Lenard scheme for two-dimensional periodic Volterra chain

Wang, Jing Ping (2009) Lenard scheme for two-dimensional periodic Volterra chain. Journal of Mathematical Physics, 50 (2). 023506. ISSN 0022-2488 . (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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We prove that for compatible weakly nonlocal Hamiltonian and symplectic operators, hierarchies of infinitely many commuting local symmetries and conservation laws can be generated under some easily verified conditions no matter whether the generating Nijenhuis operators are weakly nonlocal or not. We construct a recursion operator of the two-dimensional periodic Volterra chain from its Lax representation and prove that it is a Nijenhuis operator. Furthermore we show that this system is a (generalized) bi-Hamiltonian system. Rather surprisingly, the product of its weakly nonlocal Hamiltonian and symplectic operators gives rise to the square of the recursion operator.

Item Type: Article
Additional information: Article Number: 023506
Uncontrolled keywords: conservation laws; Korteweg-de Vries equation; mathematical operators; nonlinear equations; Volterra equations
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Jing Ping Wang
Date Deposited: 27 Oct 2009 14:29
Last Modified: 11 Jun 2014 09:02
Resource URI: https://kar.kent.ac.uk/id/eprint/23121 (The current URI for this page, for reference purposes)
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