Naslov
Gauge transformations and symmetries of integrable systems

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

Izvornik
Journal of Physics A Mathematical & Theoretical (1751-8113) 40 (2007), 40; 12227-12241

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
gauge transformations; infinitesimal symmetries; integrable systems

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA