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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}}, & &…
Commutator-errors in large-eddy simulation
Bernard J. Geurts, Darryl D. Holm
A new formulation is derived for the commutator-errors in large-eddy simulation of incompressible flow. These commutator-errors arise from the application of non-uniform filters to…
Integrable and non-integrable equations with peakons
A. Degasperis, D. D. Holm, A. N. W. Hone
We consider a one-parameter family of non-evolutionary partial differential equations which includes the integrable Camassa-Holm equation and a new equation first isolated by Degas…
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[…
Mean effects of turbulence on elliptic instability in fluids
Bruce R. Fabijonas, Darryl D. Holm
Elliptic instability in fluids is discussed in the context of the Lagrangian-averaged Navier-Stokes-alpha (LANS) turbulence model. This model preserves the Craik-Criminale (CC)…