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Full-Text Articles in Non-linear Dynamics
Euler Equations On A Semi-Direct Product Of The Diffeomorphisms Group By Itself, Joachim Escher, Rossen Ivanov, Boris Kolev
Euler Equations On A Semi-Direct Product Of The Diffeomorphisms Group By Itself, Joachim Escher, Rossen Ivanov, Boris Kolev
Articles
The geodesic equations of a class of right invariant metrics on the semi-direct product of two Diff(S) groups are studied. The equations are explicitly described, they have the form of a system of coupled equations of Camassa-Holm type and possess singular (peakon) solutions. Their integrability is further investigated, however no compatible bi-Hamiltonian structures on the corresponding dual Lie algebra are found.
Smooth And Peaked Solitons Of The Camassa-Holm Equation And Applications, Darryl Holm, Rossen Ivanov
Smooth And Peaked Solitons Of The Camassa-Holm Equation And Applications, Darryl Holm, Rossen Ivanov
Articles
The relations between smooth and peaked soliton solutions are reviewed for the Camassa- Holm (CH) shallow water wave equation in one spatial dimension. The canonical Hamiltonian formulation of the CH equation in action-angle variables is expressed for solitons by using the scattering data for its associated isospectral eigenvalue problem, rephrased as a Riemann- Hilbert problem. The momentum map from the action-angle scattering variables T∗(TN) to the flow momentum (X∗) provides the Eulerian representation of the N-soliton solution of CH in terms of the scattering data and squared eigenfunctions of its isospectral eigenvalue problem. The …