scholarly journals Non-local hydrodynamics as a slow manifold for the one-dimensional kinetic equation

2020 ◽  
Author(s):  
Florian Kogelbauer
Keyword(s):  
Kinetic Equation ◽  
Slow Manifold ◽  
One Dimensional ◽  
Non Local ◽  
The One

scholarly journals Uniqueness of one-dimensional Néel wall profiles

2016 ◽  
Vol 472 (2187) ◽  
pp. 20150762 ◽  
Author(s):  
Cyrill B. Muratov ◽  
Xiaodong Yan
Keyword(s):  
Domain Wall ◽  
Energy Functional ◽  
Wall Structure ◽  
One Dimensional ◽  
Uniform Estimates ◽  
Limiting Behaviour ◽  
Non Local ◽  
The One ◽  
Wall Profile ◽  
Domain Wall Structure

We study the domain wall structure in thin uniaxial ferromagnetic films in the presence of an in-plane applied external field in the direction normal to the easy axis. Using the reduced one-dimensional thin-film micromagnetic model, we analyse the critical points of the obtained non-local variational problem. We prove that the minimizer of the one-dimensional energy functional in the form of the Néel wall is the unique (up to translations) critical point of the energy among all monotone profiles with the same limiting behaviour at infinity. Thus, we establish uniqueness of the one-dimensional monotone Néel wall profile in the considered setting. We also obtain some uniform estimates for general one-dimensional domain wall profiles.

Solution of Generalized Jaynes-Cummings Model for many Particle Systems

2013 ◽  
Vol 481 ◽  
pp. 272-277
Author(s):  
N.N. Jr. Bogolubov ◽  
M.Yu. Rasulova ◽  
I.A. Tishabaev
Keyword(s):  
Kinetic Equation ◽  
Linear Equation ◽  
Schrodinger Equation ◽  
Particle Systems ◽  
Cavity Field ◽  
One Dimensional ◽  
Generalized Kinetic Equation ◽  
The One ◽  
The Given ◽  
Multi Mode

We consider the dynamics of a system consisting of N two-level atoms interacting with a multi-mode cavity field. For the given system, the generalized kinetic equation is obtained and conditions are given under which its solution is reduced to solution of a linear equation, and of the one-dimensional nonlinear Schrodinger equation, respectively.

QUANTUM DYNAMICS OF TWO-LEVEL ATOMS INTERACTING WITH AN ELECTROMAGNETIC FIELD

2014 ◽  
Vol 28 (08) ◽  
pp. 1450060
Author(s):  
N. N. BOGOLUBOV ◽  
M. Yu. RASULOVA ◽  
I. A. TISHABOEV
Keyword(s):  
Electromagnetic Field ◽  
Kinetic Equation ◽  
Linear Equation ◽  
Quantum Dynamics ◽  
Cavity Field ◽  
One Dimensional ◽  
Generalized Kinetic Equation ◽  
The One ◽  
The Given ◽  
Multi Mode

We consider the dynamics of a system consisting of N two-level atoms interacting with a multi-mode cavity field. For the given system, the generalized kinetic equation (GKE) is obtained and conditions are given under which its solution is reduced to solution of a linear equation, and of the one-dimensional nonlinear Schrödinger equation, respectively.

scholarly journals Non-local Problems with Integral Displacement for Highorder Parabolic Equations

2021 ◽  
Vol 36 ◽  
pp. 14-28
Author(s):  
A.I. Kozhanov ◽  
◽  
A.V. Dyuzheva ◽  
◽  
Keyword(s):  
Parabolic Equations ◽  
High Order ◽  
Multidimensional Case ◽  
Integral Conditions ◽  
Spatial Variables ◽  
One Dimensional ◽  
Linear Parabolic Equations ◽  
Local Problems ◽  
Non Local ◽  
The One

The aim of this paper is to study the solvability of solutions of non-local problems with integral conditions in spatial variables for high-order linear parabolic equations in the classes of regular solutions (which have all the squared derivatives generalized by S. L. Sobolev that are included in the corresponding equation) . Previously, similar problems were studied for high-order parabolic equations, either in the one-dimensional case, or when certain conditions of smallness on the coefficients are met equations. In this paper, we present new results on the solvability of non-local problems with integral spatial variables for high-order parabolic equations a) in the multidimensional case with respect to spatial variables; b) in the absence of smallness conditions. The research method is based on the transition from a problem with non-local integral conditions to a problem with classical homogeneous conditions of the first or second kind on the side boundary for a loaded integro-differential equation. At the end of the paper, some generalizations of the obtained results will be described.

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