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Gauge transformations and symmetries of integrable systems (CROSBI ID 141323)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Fukuyama, T. ; Kamimura, K. ; Krešić-Jurić, Saša ; Meljanac, Stjepan Gauge transformations and symmetries of integrable systems // Journal of physics. A, Mathematical and theoretical, 40 (2007), 40; 12227-12241

Podaci o odgovornosti

Fukuyama, T. ; Kamimura, K. ; Krešić-Jurić, Saša ; Meljanac, Stjepan

engleski

Gauge transformations and symmetries of integrable systems

We analyze several integrable systems in zero-curvature form within the framework of $SL(2, \R)$ invariant gauge theory. In the Drinfeld-Sokolov gauge we derive a two-parameter family of nonlinear evolution equations which as special cases include the Kortweg-de Vries (KdV) and Harry Dym equations. We find residual gauge transformations which lead to infinitesimal symmetries of this family of equations. For KdV and Harry Dym equations we find an infinite hierarchy of such symmetry transformations, and we investigate their relation with local conservation laws, constants of the motion and the bi-Hamiltonian structure of the equations. Applying successive gauge transformations of Miura type we obtain a sequence of gauge equivalent integrable systems, among them the modified KdV and Calogero KdV equations.

gauge transformations; infinitesimal symmetries; integrable systems

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Podaci o izdanju

40 (40)

2007.

12227-12241

objavljeno

1751-8113

Povezanost rada

Matematika

Indeksiranost