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MiS Preprint
50/2008

Geodesic Flow on Extended Bott-Virasoro Group and Generalized Two Component Peakon Type Dual Systems

Partha Guha

Abstract

This paper discusses several algorithmic ways of constructing integrable evolution equations based on Lie algebraic structure. We derive, in a pedagogical style, a large class of two component peakon type dual systems from their two component soliton equations counter part. We study the essential aspects of Hamiltonian flows on coadjoint orbits of the centrally extended semidirect product group $\widehat{Diff(S^1)\ltimes C^{\infty}}(S^1)$ to give a systematic derivation of the dual counter parts of various two component of integrable systems, viz., the dispersive water wave equation, the Kaup-Boussinesq system and the Broer-Kaup system, using moment of inertia operators method and the (frozen) Lie-Poisson structure. This paper essentially gives Lie algebraic explanation of Olver-Rosenau's paper.

Received:
Jul 28, 2008
Published:
Jul 29, 2008
MSC Codes:
53A07, 53B50
Keywords:
geodesic flow, Sobolev norm, frozen Lie-Poisson structure

Related publications

inJournal
2008 Repository Open Access
Partha Guha

Geodesic flow on extended Bott-Virasoro group and generalized two component Peakon type dual systems

In: Reviews in mathematical physics, 20 (2008) 10, pp. 1191-1208