33 citations · 123 across the 20 of their papers we have counts for
20 papers
Semiclassical approach to the nonlocal nonlinear Schrödinger equation with a non-Hermitian term
A. E. Kulagin, A. V. Shapovalov
The nonlinear Schödinger equation (NLSE) with a non-Hermitian term is the model for various phenomena in nonlinear open quantum systems. We deal with the Cauchy problem for the non…
Harmonic oscillator coherent states from the orbit theory standpoint
A. I. Breev, A. V. Shapovalov
We study the known coherent states of a quantum harmonic oscillator from the standpoint of the original developed noncommutative integration method for linear partial differential…
Analytical description of the diffusion in a cellular automaton with the Margolus neighbourhood in terms of the two-dimensional Markov chain
Anton Kulagin, Alexander Shapovalov
The one-parameter two-dimensional cellular automaton with the Margolus neighbourhood is analyzed based on the considering the projection of the stochastic movements of a single par…
Family of asymptotic solutions to the two-dimensional kinetic equation with a nonlocal cubic nonlinearity
Alexander V. Shapovalov, Anton E. Kulagin, Sergei A. Siniukov
We apply the original semiclassical approach to the kinetic ionization equation with the nonlocal cubic nonlinearity in order to construct the family of its asymptotic solutions. T…
Semiclassical approach to the nonlocal kinetic model of metal vapor active media
Alexander V. Shapovalov, Anton E. Kulagin
A semiclassical approach based on the WKB-Maslov method is developed for the kinetic ionization equation in dense plasma with approximations characteristic of metal vapor active me…
Noncommutative reduction of the nonlinear Schrödinger equation on Lie groups
A. I. Breev, A. V. Shapovalov, D. M. Gitman
We propose a new approach that allows one to reduce nonlinear equations on Lie groups to equations with a fewer number of independent variables for finding particular solutions of…