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 τ for these equations are simply derived within our formalism. Furthermore, certain new functionsT 12 are introduced, which algorithmically imply recursion operators Φ12. 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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Fokas, A.S., Santini, P.M. Recursion operators and bi-Hamiltonian structures in multidimensions. II. Commun.Math. Phys. 116, 449–474 (1988). https://doi.org/10.1007/BF01229203
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DOI: https://doi.org/10.1007/BF01229203