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

Partha Guha

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Submission date: 28. Jul. 2008
Pages: 21
published in: Reviews in mathematical physics, 20 (2008) 10, p. 1191-1208 
DOI number (of the published article): 10.1142/S0129055X08003523
Bibtex
MSC-Numbers: 53A07, 53B50
Keywords and phrases: geodesic flow, Sobolev norm, frozen Lie-Poisson structure
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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 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 [Preprint 50/2008].