Euler-Poincaré Formalism of Coupled KdV Type Systems and Diffeomorphism Group on S1
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P. Guha
Abstract
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 
, 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 .
© Heldermann Verlag
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Articles in the same Issue
- On Additive Almost Continuous Functions Under
- Maximal Solutions and Existence Theory for Fuzzy Differential and Integral Equations
- Projections in Weakly Compactly Generated Banach Spaces and Chang's Conjecture
- Dominated Convergence and Stone-Weierstrass Theorem
- Optimality Conditions and Duality for Multiobjective Control Problems
- On the Convergence of Sequences of Functions which are Discontinuous on Countable Sets
- Euler-Poincaré Formalism of Coupled KdV Type Systems and Diffeomorphism Group on S1
- Stability Analysis and Comparison of the Models for Carcinogenesis Mutations in the Case of Two Stages of Mutations
