Recursion operators and bi-Hamiltonian structures in multidimensions. II |
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Authors: | A S Fokas P M Santini |
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Institution: | (1) Department of Mathematics and Computer Science and Institute for Nonlinear Studies, Clarkson University, 13676 Potsdam, NY, USA;(2) Present address: Dipartimento di Fisica, Universita di Roma, La Sapienza, J-00185 Roma, Italy |
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Abstract: | We analyze further the algebraic properties of bi-Hamiltonian systems in two spatial and one temporal dimensions. By utilizing the Lie algebra of certain basic (starting) symmetry operators we show that these equations possess infinitely many time dependent symmetries and constants of motion. The master symmetries for these equations are simply derived within our formalism. Furthermore, certain new functionsT
12 are introduced, which algorithmically imply recursion operators 12. Finally the theory presented here and in a previous paper is both motivated and verified by regarding multidimensional equations as certain singular limits of equations in one spatial dimension. |
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