16 citations · 58 across the 6 of their papers we have counts for
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math-ph2019
The effect of a positive bound state on the KdV solution. A case study
Alexei Rybkin
We consider a slowly decaying oscillatory potential such that the corresponding 1D Schrödinger operator has a positive eigenvalue embedded into the absolutely continuous spectrum.…
math-ph2019
On classical solutions of the KdV equation
Alexei Rybkin, Sergei Grudsky
\begin{abstract} We show that if the initial profile for the Korteweg-de Vries (KdV) equation is essentially semibounded from below and $\int^{\infty }x^{5/2}\l…
math-ph2017★ 12 cited
KdV equation beyond standard assumptions on initial data
Alexei Rybkin
We show that the Cauchy problem for the KdV equation can be solved by the inverse scattering transform (IST) for any initial data bounded from below, decaying sufficiently rapidly…