576 citations · 1.9k across the 50 of their papers we have counts for
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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…
The Complex Geometry of Weak Piecewise Smooth Solutions of Integrable Nonlinear PDE's of Shallow Water and Dym Type
Mark S. Alber, Roberto Camassa, Yuri N. Fedorov +2
An extension of the algebraic-geometric method for nonlinear integrable PDE's is shown to lead to new piecewise smooth weak solutions of a class of -component systems of nonline…
Dissipation induced Instabilities and the Mechanical Laser
Marcel G. Clerc, Jerrold E. Marsden
We study the 1:1 resonance for perturbed Hamiltonian systems with small dissipative and energy injection terms. These perturbations of the 1:1 resonance exhibit dissipation induced…
An Optimal Control Formulation for Inviscid Incompressible Ideal Fluid Flow
A. M. Bloch, P. E. Crouch, D. D. Holm +1
In this paper we consider the Hamiltonian formulation of the equations of incompressible ideal fluid flow from the point of view of optimal control theory. The equations are compar…