7 citations · 12 across the 7 of their papers we have counts for
7 papers
Dispersive Shock Wave, Generalized Laguerre Polynomials and Asymptotic Solitons of the Focusing Nonlinear Schrödinger Equation
Vladimir Kotlyarov, Alexander Minakov
We consider dispersive shock wave to the focusing nonlinear Schrödinger equation generated by a discontinuous initial condition which is periodic or quasi-periodic on the left semi…
A Matrix Baker-Akhiezer Function Associated with the Maxwell-Bloch Equations and their Finite-Gap Solutions
Vladimir P. Kotlyarov
The Baker-Akhiezer (BA) function theory was successfully developed in the mid 1970s. This theory brought very interesting and important results in the spectral theory of almost per…
Periodic problem for the nonlinear Schroedinger equation
Vladimir Kotlyarov, Alexander Its
The paper offers the method of discovering of some class of solutions for the nonlinear Schroedinger equation. An algorithm of constructive solving of the Cauchy periodic problem w…
Modified Korteweg-de Vries equation: modulated elliptic wave and a train of asymptotic solitons
Vladimir Kotlyarov, Minakov Alexander
We study the long-time asymptotic behavior of the Cauchy problem for the modified Korteweg - de Vries equation with an initial function of the step type. This function rapidly tend…
Complete linearization of a mixed problem to the Maxwell-Bloch equations by matrix Riemann-Hilbert problem
V. Kotlyarov
Considered in this paper the Maxwell-Bloch (MB) equations became known after Lamb [1-4]. In [5] Ablowitz, Kaup and Newell proposed the inverse scattering transform (IST) to the Max…
Characteristic properties of the scattering data for the mKdV equation on the half-line
Anne Boutet de Monvel, Vladimir Kotlyarov
In this paper we describe characteristic properties of the scattering data of the compatible eigenvalue problem for the pair of differential equations related to the modified Korte…