This article is cited in 9 papers

Algebraic properties of Gardner's deformations for integrable systems

A. V. Kiselev<sup>ab

a</sup> Institut des Hautes Études Scientifiques
^b Max Planck Institute for Mathematics

Abstract: We formulate an algebraic definition of Gardner's deformations for completely integrable bi-Hamiltonian evolutionary systems. The proposed approach extends the class of deformable equations and yields new integrable evolutionary and hyperbolic Liouville-type systems. We find an exactly solvable two-component extension of the Liouville equation.

Keywords: Gardner's deformation, integrable family, adjoint system, Hamiltonian, recursion relation.

DOI: 10.4213/tmf6073

 English version: Theoretical and Mathematical Physics, 2007, 152:1, 963–976

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