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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}}, & &…
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[…
A New Integrable Equation with Peakon Solutions
A. Degasperis, D. D. Holm, A. N. W. Hone
We consider a new partial differential equation, of a similar form to the Camassa-Holm shallow water wave equation, which was recently obtained by Degasperis and Procesi using the…
R-matrix for a geodesic flow associated with a new integrable peakon equation
Darryl D. Holm, Zhijun Qiao
We use the r-matrix formulation to show the integrability of geodesic flow on an -dimensional space with coordinates , with , equipped with the co-metric $g^{ij}…