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Journals and Conferences
We show that the smooth traveling waves of the Camassa-Holm equation naturally correspond to traveling waves of the Korteweg-de Vries equation.
We develop several methods that allow us to compute all-loop partition functions in perturbative Chern-Simons theory with complex gauge group GC, sometimes in multiple ways. In the background of a… (More)
We study a family of equations defined on the space of tensor densities of weight λ on the circle and introduce two integrable PDE. One of the equations turns out to be closely related to the… (More)
We explore numerically different aspects of periodic traveling-wave solutions of the Camassa–Holm equation. In particular, the time evolution of some recently found new traveling-wave solutions and… (More)
The Hunter–Saxton equation is the Euler equation for the geodesic flow on the quotient space of the infinite-dimensional group of orientation preserving diffeomorphisms of the unit circle modulo the… (More)
We consider an integrable generalization of the nonlinear Schrödinger (NLS) equation that was recently derived by one of the authors using bi-Hamiltonian methods. This equation is related to the NLS… (More)
A supersymmetric extension of the Hunter-Saxton equation is constructed. We present its bi-Hamiltonian structure and show that it arises geometrically as a geodesic equation on the space of… (More)
We study the geometry of the space of densities Dens(M), which is the quotient space Diff(M)/Diffμ(M) of the diffeomorphism group of a compact manifold M by the subgroup of volume-preserving… (More)
A simple algoritm for the inverse scattering approach to the Camassa-Holm equation is presented.
We present an approach proving the integrability of the Camassa–Holm equation for initial data of small amplitude.