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On the one class of hyperbolic systems. (English) Zbl 1138.35360
Summary: The classification problem is solved for some type of nonlinear lattices. These lattices are closely related to the lattices of Ruijsenaars-Toda type and define the Bäcklund auto-transformations for the class of two-component hyperbolic systems.

MSC:
 35L60 First-order nonlinear hyperbolic equations 35Q55 NLS equations (nonlinear Schrödinger equations) 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems 35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
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