[Turkmath:5912] (no subject)

[Allaberen Ashyralyev]

Dear Colleagues!

You are cordially invited to the  Weekly Online  Seminar “Analysis and
Applied Mathematics” on

Date: Tuesday, December 20, 2022

Time: 14.00-15.00 (Istanbul) = 13.00-14.00 (Ghent) = 17.00-18.00 (Almaty)

Zoom link:
https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaH-lDaVYrN3l5bzJVQT09,
Conference ID: 667 827 0445, Access code: 1

Speaker: Prof. Dr. Vsevolod Sakbaev
Keldysh Institute of Applied Mathematics Russian Academy of Science,
Russian Federation.

  Title:  On the Properties of Solutions of Nonlinear Schrodinger Equation
Abstract:We consider the transformation of the initial data space of the
Cauchy problem for the focusing nonlinear Schrodinger equation with power
nonlinearity in potential ([1]- [3]). Also we study properties of the
initial-boundary value problem for a nonlinear Schrodinger equation
including terms with delay of time argument. First, we prove the local
existence for the Cauchy problem and for the initial problem. After that we
study the phenomenon of global existence as a solution of the Cauchy
problem for small powers of nonlinearity. In the case of large power of
nonlinearity the phenomenon of rise of a solution gradient blow up during a
finite time is proven. In the last case we study qualitative properties of
a solution when it approaches the boundary of its interval of existence.
Same properties are studied for the initial problem. The relation of the
gradient blow up phenomenon with the self-focusing and the destruction of
the pure quantum state are described [2]. Moreover, we define a solution
extension through the moment of a gradient blow by means of the random
process with values in the set of pure quantum states. We show that this
extension describes the destruction of a solution as the destruction of a
pure quantum state and the transition from the set of pure quantum states
into the set of mixed quantum states [3].

 References:
[1] A.D. Grekhneva & V.Zh. Sakbaev, Dynamics of a Set of Quantum States
Generated by a Nonlinear Liouville–von Neumann Equation. Computational
Mathematics & Mathematical Physics, 60:8 (2020), 1337-1347.
[2] L.S. Efremova, A.D. Grekhneva, V.Zh. Sakbaev, Phase flow generated by
Cauchy problem for nonlinear Schrodinger equation and dynamical mappings of
quantum states. Lobachevskii Journal of Mathematics, 40:10 (2019),
1455-1469.
[3] V.Zh. Sakbaev & A.D. Shiryaeva, Blow-Up of States in the Dynamics Given
by the Schrödinger Equation with a Power-Law Nonlinearity in the Potential.
Differential Equation, 58:4 (2022), 498-508.

Abstracts and forthcoming talks can be found on our webpage
https://sites.google.com/view/aam-seminars
With my best wishes
*Prof. Dr. Allaberen Ashyralyev *
*Department of Mathematics, Bahcesehir University, 34353, Istanbul, Turkey*
*  and **Near East University, Lefkoşa(Nicosia), Mersin 10 Turkey*
*Peoples' Friendship University of Russia (RUDN University),** Ul Miklukho
Maklaya 6, Moscow 117198, Russian Federation *
*Institute of Mathematics and Mathematical Modelling, 050010, Almaty,
Kazakhstan*
*e-mail: allaberen.ashyralyev at eng.bau.edu.tr
<allaberen.ashyralyev at neu.edu.tr> and **aallaberen at gmail.com
<aallaberen at gmail.com> *
 http://akademik.bahcesehir.edu.tr/web/allaberenashyralyev

https://sites.google.com/view/aam-seminars
https://content.sciendo.com/view/journals/ejaam/ejaam-overview.xml
*icaam-online.org <http://icaam-online.org>*

*https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1
<https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1>*
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://yunus.listweb.bilkent.edu.tr/pipermail/turkmath/attachments/20221216/20add93b/attachment-0001.html>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Analysis&Appl Math_Seminar_December 20.pdf
Type: application/pdf
Size: 360179 bytes
Desc: not available
URL: <http://yunus.listweb.bilkent.edu.tr/pipermail/turkmath/attachments/20221216/20add93b/attachment-0001.pdf>