Euler-Poincare formalism of coupled KdV type system and diffeomorphism group on S1

• Autorzy: Guha P.
• Języki publikacji: EN

Abstrakty

EN

This paper describes a wide class of coupled KdV equations. The first set of equations directly follow from the geodesic flows on the Bott-Virasoro group with a complex field. But the set of 2-component systems of nonlinear evolution equations, which includes dispersive water waves, Ito's equation, many other known and unknown equations, follow from the geodesic flows of the right invariant L2 metric on the semidirect product group [wzór], where Diff(S1) is the group of orientation preserving diffeomorphisms on a circle. We compute the Lie-Poisson brackets of the Antonowicz-Fordy system, and the mode expansion of these beackets yield the twisted Heisenberg-Virasoro algebra. We also give an outline to study geodesic flows of a H1 metric on [wzór].

Słowa kluczowe

EN

diffeomorphism; geodesic flows; coupled KdV equations; Bott-Virasoro group; twisted Heisenberg-Virasoro algebra

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2005
• Tom: Vol. 11, nr 2
• Strony: 261--282
• Opis fizyczny: Bibliogr.30 poz.

Twórcy

autor

Guha P.

• S.N. Bose National Centre for Basic Sciences, JD Block, Sector-3, Salt Lake Calcutta-700098, India
• Department of Mathematics, University of Colorado at Colorado Springs, 1420 Austin Bluffs Parkway, Colorado Springs, Colorado 80933-7150, USA

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