Wang, J.P. (2009) Lenard scheme for two-dimensional periodic Volterra chain. Journal of Mathematical Physics, 50 (2). 023506. ISSN 0022-2488 .
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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.
|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:||27 Oct 2009 14:29|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/23121 (The current URI for this page, for reference purposes)|
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