44 citations · 102 across the 8 of their papers we have counts for
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math.AP2019★ 10 cited
Method for solving hyperbolic systems with initial data on non-characteristic manifolds with applications to the shallow water wave equations
Alexei Rybkin
We are concerned with hyperbolic systems of order-one linear PDEs originated on non-characteristic manifolds. We put forward a simple but effective method of transforming such init…
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…