245 citations · 667 across the 24 of their papers we have counts for
7 papers · 1 filter
Geodesic flows on semidirect-product Lie groups: geometry of singular measure-valued solutions
Darryl D. Holm, Cesare Tronci
The EPDiff equation (or dispersionless Camassa-Holm equation in 1D) is a well known example of geodesic motion on the Diff group of smooth invertible maps (diffeomorphisms). Its re…
Vlasov moments, integrable systems and singular solutions
John Gibbons, Darryl D Holm, Cesare Tronci
The Vlasov equation for the collisionless evolution of the single-particle probability distribution function (PDF) is a well-known Lie-Poisson Hamiltonian system. Remarkably, the o…
Hasimoto Transformation and Vortex Soliton Motion Driven by Fluid Helicity
Darryl D. Holm, Samuel N. Stechmann
Vorticity filament motions with respect to the Dirac bracket of Rasetti and Regge [1975] are known to be related to the nonlinear Schrödinger equation by the Hasimoto transformatio…
An integrable hierarchy, parametric solution and traveling wave solution
Darryl D. Holm, Zhijun Qiao
This paper gives an integrable hierarchy of nonlinear evolution equations. In this hierarchy there are the following representative equations: \beqq & & u_t=\pa^5_x u^{-{2/3}}, & &…
On the non-integrability of a fifth order equation with integrable two-body dynamics
D. D. Holm, A. N. W. Hone
We consider the fifth order partial differential equation (PDE) , which is a generalization of the integrab…
Integrable hierarchy, constrained systems, and parametric and peaked stationary solutions
Darryl D. Holm, Zhijun Qiao
This paper gives a new integrable hierarchy of nonlinear evolution equations. The DP equation: , proposed recently by Desgaperis and Procesi \cite{DP[…