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Momentum Maps and Measure-valued Solutions (Peakons, Filaments and Sheets) for the EPDiff Equation
Darryl D. Holm, Jerrold E. Marsden
We study the dynamics of measure-valued solutions of what we call the EPDiff equations, standing for the {\it Euler-Poincaré equations associated with the diffeomorphism group (of…
Rotating Concentric Circular Peakons
Darryl D. Holm, Vakhtang Putkaradze, Samuel N. Stechmann
We study invariant manifolds of measure-valued solutions of the partial differential equation for geodesic flow of a pressureless fluid. These solutions describe interaction dynami…
On asymptotically equivalent shallow water wave equations
H. R. Dullin, G. A. Gottwald, D. D. Holm
The integrable 3rd-order Korteweg-de Vries (KdV) equation emerges uniquely at linear order in the asymptotic expansion for unidirectional shallow water waves. However, at quadratic…