Algebraic properties of Gardner's deformations for integrable systems

A. B. Borisov; A. Karasu; A. V. Kiselev; A. V. Kiselev; A. V. Kiselev; A. V. Zhiber; B. A. Kupershmidt; D. K. Demskoi; E. Getzler; G. Carlet; I. Krasil’shchik; M. Gerstenhaber; M. V. Pavlov; P. Kersten; P. Kersten; P. Labelle; P. Mathieu; P. Mathieu; R. M. Miura; S. Igonin; V. G. Drinfel’d

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Algebraic properties of Gardner's deformations for integrable systems

Authors: A. B. Borisov
A. Karasu
A. V. Kiselev
A. V. Kiselev
A. V. Kiselev
A. V. Zhiber
B. A. Kupershmidt
D. K. Demskoi
E. Getzler
G. Carlet
I. Krasil’shchik
M. Gerstenhaber
M. V. Pavlov
P. Kersten
P. Kersten
P. Labelle
P. Mathieu
P. Mathieu
R. M. Miura
S. Igonin
V. G. Drinfel’d
Publication date: 1 January 2007
Publisher: 'Springer Science and Business Media LLC'
Doi

Abstract

An algebraic definition of Gardner's deformations for completely integrable bi-Hamiltonian evolutionary systems is formulated. The proposed approach extends the class of deformable equations and yields new integrable evolutionary and hyperbolic Liouville-type systems. An exactly solvable two-component extension of the Liouville equation is found.Comment: Proc. conf. "Nonlinear Physics: Theory and Experiment IV" (Gallipoli, 2006); Theor. Math. Phys. (2007) 151:3/152:1-2, 16p. (to appear