24 citations · 67 across the 9 of their papers we have counts for
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Initial Value Problem of the Whitham Equations for the Camassa-Holm Equation
Tamara Grava, V. U. Pierce, Fei-Ran Tian
We study the Whitham equations for the Camassa-Holm equation. The equations are neither strictly hyperbolic nor genuinely nonlinear. We are interested in the initial value problem…
Reciprocal transformations and flat metrics on Hurwitz spaces
S. Abenda, T. Grava
We consider hydrodynamic systems which possess a local Hamiltonian structure of Dubrovin-Novikov type. To such a system there are also associated an infinite number of nonlocal Ham…
Riemann-Hilbert problem for the small dispersion limit of the KdV equation and linear overdetermined systems of Euler-Poisson-Darboux type
T. Grava
We study the Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion and with monotonically increasing initial data using the Riemann-Hilbert (RH) approach. T…
From the solution of the Tsarev system to the solution of the Whitham equations
T. Grava
We study the Cauchy problem for the Whitham modulation equations for monotone increasing smooth initial data. The Whitham equations are a collection of one-dimensional quasi-linear…