Geodesic flows, bi-Hamiltonian structure and coupled KdV type systems

Partha Guha

doi:10.1016/j.jmaa.2004.12.060

Geodesic flows, bi-Hamiltonian structure and coupled KdV type systems

Partha Guha

Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

We show that all the Antonowicz-Fordy type coupled KdV equations have the same symmetry group and similar bi-Hamiltonian structures. It turns out that their configuration space is Diff(S¹) ⋉ C (S¹), where Diff(S¹), is the Bott-Virasoro group of orientation preserving diffeomorphisms of the circle, and all these systems can be interpreted as equations of a geodesic flow with respect to L² metric on the semidirect product space Diff(S¹) ⋉ C (S¹).

Original language	British English
Pages (from-to)	45-56
Number of pages	12
Journal	Journal of Mathematical Analysis and Applications
Volume	310
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2004.12.060
State	Published - 1 Oct 2005

Keywords

Bott-Virasoro group
Coupled KdV equations
Diffeomorphism
Geodesic flows
Semi-direct product

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10.1016/j.jmaa.2004.12.060

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AB - We show that all the Antonowicz-Fordy type coupled KdV equations have the same symmetry group and similar bi-Hamiltonian structures. It turns out that their configuration space is Diff(S1) ⋉ C (S1), where Diff(S1), is the Bott-Virasoro group of orientation preserving diffeomorphisms of the circle, and all these systems can be interpreted as equations of a geodesic flow with respect to L2 metric on the semidirect product space Diff(S1) ⋉ C (S1).

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KW - Coupled KdV equations

KW - Diffeomorphism

KW - Geodesic flows

KW - Semi-direct product

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Geodesic flows, bi-Hamiltonian structure and coupled KdV type systems

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Keywords

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