A Semiclassical Approach to the Nonlocal Nonlinear Schrödinger Equation with a Non-Hermitian Term; Mathematics; Vol. 12, iss. 4

A Semiclassical Approach to the Nonlocal Nonlinear Schrödinger Equation with a Non-Hermitian Term; Mathematics; Vol. 12, iss. 4

Bibliographic Details
Parent link:Mathematics.— .— Basel: MDPI AG
Vol. 12, iss. 4.— 2024.— Article number 580, 22 p.
Main Author: Kulagin A. E. Anton Evgenievich
Corporate Author: National Research Tomsk Polytechnic University
Other Authors: Shapovalov A. V. Aleksandr Vasilyevich
Summary:Title screen
The nonlinear Schrödinger 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 nonlocal generalization of multidimensional NLSE with a non-Hermitian term. Using the ideas of the Maslov method, we propose the method of constructing asymptotic solutions to this equation within the framework of semiclassically concentrated states. The semiclassical nonlinear evolution operator and symmetry operators for the leading term of asymptotics are derived. Our approach is based on the solutions of the auxiliary dynamical system that effectively linearizes the problem under certain algebraic conditions. The formalism proposed is illustrated with the specific example of the NLSE with a non-Hermitian term that is the model of an atom laser. The analytical asymptotic solution to the Cauchy problem is obtained explicitly for this example.
Текстовый файл
Language:English
Published: 2024
Subjects:
электронный ресурс
труды учёных ТПУ
semiclassically concentrated solutions
Maslov’s complex germ method
open quantum systems; asymptotic solution
dissipation; atom laser
Online Access:http://earchive.tpu.ru/handle/11683/132477
https://doi.org/10.3390/math12040580
Format: Electronic Book Chapter
KOHA link:https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=672132

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