Attractors of nonlinear Hamiltonian partial differential equations

AI Komech, EA Kopylova - Russian Mathematical Surveys, 2020 - iopscience.iop.org
This is a survey of the theory of attractors of nonlinear Hamiltonian partial differential
equations since its appearance in 1990. Included are results on global attraction to …

[PDF][PDF] A survey on asymptotic stability of ground states of nonlinear Schrodinger equations II

S Cuccagna, M Maeda - arxiv preprint arxiv:2009.00573, 2020 - arxiv.org
arxiv:2009.00573v1 [math.AP] 1 Sep 2020 Page 1 arxiv:2009.00573v1 [math.AP] 1 Sep 2020
A survey on asymptotic stability of ground states of nonlinear Schrödinger equations II Scipio …

[BOOK][B] Lectures on quantum mechanics and attractors

A Komech - 2022 - books.google.com
This book gives a concise introduction to Quantum Mechanics with a systematic, coherent,
and in-depth explanation of related mathematical methods from the scattering theory and the …

[BOOK][B] Quantum mechanics: genesis and achievements

A Komech - 2012 - books.google.com
The focus of the present work is nonrelativistic and relativistic quantum mechanics with
standard applications to the hydrogen atom. The author has aimed at presenting quantum …

On stability of small solitons of the 1-D NLS with a trap** delta potential

S Cuccagna, M Maeda - SIAM Journal on Mathematical Analysis, 2019 - SIAM
We consider a nonlinear Schrödinger equation (NLS) with a very general nonlinear term
and with a trap** δ potential on the line. We then discuss the asymptotic behavior of all its …

Global attraction to solitary waves for a nonlinear Dirac equation with mean field interaction

A Komech, A Komech - SIAM journal on mathematical analysis, 2010 - SIAM
We consider a U(1)-invariant nonlinear Dirac equation in dimension n\geq1, interacting with
itself via the mean field mechanism. We analyze the long-time asymptotics of solutions and …

On global attraction to solitary waves for the Klein–Gordon field coupled to several nonlinear oscillators

A Komech, A Komech - Journal de mathématiques pures et appliquées, 2010 - Elsevier
The global attraction is established for the U (1)-invariant Klein–Gordon equation in one
dimension coupled to a finite number of nonlinear oscillators. Each finite energy solution is …

On quantum jumps and attractors of the Maxwell–Schrödinger equations

AI Komech - Annales mathématiques du Québec, 2022 - Springer
Our goal is the discussion of the problem of mathematical interpretation of basic postulates
(or “principles”) of Quantum Mechanics: transitions to quantum stationary orbits, the wave …

Weak attractor of the Klein-Gordon field in discrete space-time interacting with a nonlinear oscillator

A Comech - arxiv preprint arxiv:1203.3233, 2012 - arxiv.org
We consider the U (1)-invariant nonlinear Klein-Gordon equation in discrete space and
discrete time, which is the discretization of the nonlinear continuous Klein-Gordon equation …

Global attractor for 1D Dirac field coupled to nonlinear oscillator

E Kopylova, A Komech - Communications in Mathematical Physics, 2020 - Springer
Global attraction to solitary waves is proved for a model U (1) U (1)-invariant nonlinear 1D
Dirac equation coupled to a nonlinear oscillator: each finite energy solution converges as t …