44 citations · 151 across the 23 of their papers we have counts for
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nlin.SI2011★ 1 cited
Spatial Analyticity of solutions to integrable systems. I. The KdV case
Alexei Rybkin
We are concerned with the Cauchy problem for the KdV equation for nonsmooth locally integrable initial profiles q's which are, in a certain sense, essentially bounded from below an…
nlin.SI2011★ 2 cited
Singular Miura type initial profiles for the KdV equation
Sergei Grudsky, Alexei Rybkin
We show that the KdV flow evolves any real singular initial profile q of the form q=r'+r^2, where r\inL_{loc}^2, r|_{R_+}=0 into a meromorphic function with no real poles.
nlin.SI2010★ 19 cited
The Hirota τ-function and well-posedness of the KdV equation with an arbitrary step like initial profile decaying on the right half line
Alexei Rybkin
We are concerned with the Cauchy problem for the KdV equation on the whole line with an initial profile V_0 which is decaying sufficiently fast at +\infty and arbitrarily enough (i…