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Discrete wave turbulence of rotational capillary water waves
Adrian Constantin, Elena Kartashova, Erik Wahlén
We study the discrete wave turbulent regime of capillary water waves with constant non-zero vorticity. The explicit Hamiltonian formulation and the corresponding coupling coefficie…
Integrability of invariant metrics on the diffeomorphism group of the circle
Adrian Constantin, Boris Kolev
Each H^k Sobolev inner product defines a Hamiltonian vector field X_k on the regular dual of the Lie algebra of the diffeomorphism group of the circle. We show that only X_0 and X_…
Nearly-Hamiltonian Structure for Water Waves with Constant Vorticity
Adrian Constantin, Rossen I. Ivanov, Emil M. Prodanov
We show that the governing equations for two-dimensional gravity water waves with constant non-zero vorticity have a nearly-Hamiltonian structure, which becomes Hamiltonian for ste…
On the inverse scattering approach to the Camassa-Holm equation
Adrian Constantin, Jonatan Lenells
A simple algorithm for the inverse scattering approach to the Camassa-Holm equation is presented.
Geodesic Flow on the Diffeomorphism Group of the circle
Adrian Constantin, Boris Kolev
We show that certain right-invariant metrics endow the infinite-dimensional Lie group of all smooth orientation-preserving diffeomorphisms of the circle with a Riemannian structure…
Least action principle for an integrable shallow water equation
Adrian Constantin, Boris Kolev
For an integrable shallow water equation we describe a geometrical approach showing that any two nearby fluid configurations are successive states of a unique flow minimizing the k…