The algebraic structure of zero curvature representations and application to coupled KdV systems

The author first establishes an algebraic structure related to zero curvature representations and propose a new approach for calculating symmetry algebras of integrable systems. Then he deduces a hierarchy of nonisospectral flows associated with coupled KdV systems from a spectral problem with the Laurent polynomial dependent form of the spectral parameter. Furthermore, the commutator relations of Lax operators corresponding to isospectral and nonisospectral flows are worked out according to this algebraic structure, and thus a symmetry algebra for coupled KdV systems is engendered from this general theory.

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