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Dirac structures of integrable evolution equations
Affiliation:1. School of Science, Hangzhou Dianzi University, Hangzhou, Zhejiang, 310018, P. R. China;2. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620-5700, USA;3. International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa;4. School of Information Engineering, Hangzhou Dianzi University, Hangzhou, Zhejiang, 310018, P. R. China;5. School of Mathematics and Physical Science, Xuzhou Institute of Technology, Xuzhou, Jiangsu, 221111, P. R. China
Abstract:An algebraic theory of Dirac structures is presented, enclosing finite-dimensional pre-symplectic and Poisson structures, as well as their infinite-dimensional analogs determined by local operators. The generalized Lenard scheme of integrability is considered together with examples of its action.
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