44 citations · 151 across the 23 of their papers we have counts for
4 papers · 1 filter
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…
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.
A Haar-type Approximation and a New Numerical Schema for the Korteweg-de Vries Equation
Jason Baggett, Odile Bastille, Alexei Rybkin
We discuss a new numerical schema for solving the initial value problem for the Korteweg-de Vries equation for large times. Our approach is based upon the Inverse Scattering Transf…
On the determinant formula in the inverse scattering procedure with a partially known steplike potential
Odile Bastille, Alexei Rybkin
We are concerned with the inverse scattering problem for the full line Schrödinger operator with a steplike potential a priori known on $\Reals_+=(0,\infty…