

Preprint 50/2008
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].