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math-ph2022★ 7 cited
The inverse scattering transform for weak Wigner-von Neumann type potentials
Sergei Grudsky, Alexei Rybkin
In the context of the Cauchy problem for the Korteweg-de Vries equation we extend the inverse scattering transform to initial data that behave at plus infinity like a sum of Wigner…
math-ph2019★ 17 cited
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-ph2003★ 41 cited
On a quaternionic Maxwell equation for the time-dependent electromagnetic field in a chiral medium
Sergei M. Grudsky, Kira V. Khmelnytskaya, Vladislav V. Kravchenko
Maxwell's equations for the time-dependent electromagnetic field in a homogeneous chiral medium are reduced to a single quaternionic equation. Its fundamental solution satisfying t…