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Multi-component Volterra and Toda type integrable equations. (English) Zbl 0983.37082

Summary: Multi-component integrable analogs related to the Jordan triple systems (JTS) are constructed for the Volterra equation. Differential-difference substitutions lead to multi-component Toda type lattices. Associated equations generalize the derivative nonlinear Schrödinger equation. Multi-component master symmetries (both partial differential and differential difference ones) and zero curvature representations for lattice equations written in terms of the superstructure Lie algebra of the JTS arise for the first time.

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K60 Lattice dynamics; integrable lattice equations
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