Algebraic properties of Gardner’s deformations for integrable systems |
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| Authors: | A V Kiselev |
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| Institution: | (1) Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111 Bonn, Germany;(2) Institut des Hautes études Scientifiques, Le Bois-Marie 35, Route de Chartres, F-91440 Bures-sur-Yvette, France |
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| 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.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 1, pp. 101–117, July, 2007. |
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| Keywords: | Gardner’ s deformation integrable family adjoint system Hamiltonian recursion relation |
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