Attraction to Solitary Waves
and Related Aspects of Physics
Miniworkshop at the
Mathematisches Forschungsinstitut Oberwolfach
February 10 - 16, 2008
On the web:
/~comech/proposals/oberwolfach-2008/
The PDF version is at
/~comech/proposals/oberwolfach-2008/oberwolfach-2008.pdf
Organizers
- Vladimir Buslaev, buslaev@mph.phys.spbu.ru, St.Petersburg University
- Andrew Comech, comech@math.tamu.edu, Texas A&M University, College Station
- Alexander Komech, alexander.komech@univie.ac.at, University of Vienna
- Boris Vainberg, brvainbe@email.uncc.edu, UNC at Charlotte
Program of the miniworkshop
The miniworkshop is based on several minicourses
which will cover both the basics of the stability theory for
solitary waves and the related physical effects,
allowing immediate interaction of ideas from Mathematics and Physics.
Schedule
Schedule of lectures
- Breakfast: 8:00-9:00
- Lectures, talks: 9-12:30
- Lunch: 12:30-1:30
- Break for discussions and hiking: 1:30-4
- Talks: 4-6:30
- Dinner: 6:30-7:30 p.m
Wednesday afternoon: an excursion to
the Black Forest to a restaurant - sturdy footwear is recommended.
Minicourses
- Asymptotic stability of solitary waves in nonlinear Schrödinger equation
(Vladimir Buslaev) 4 hours
- Analytic Perturbation Theory and Renormalization Analysis of Matter
coupled to quantized radiation
(Marcel Griesemer)
3 hours
- Nonrelativistic QED: Anomalous magnetic moment
(Herbert Spohn)
2 hours
- Scattering in nonrelativistic QFT
(Jan Derezinski)
4 hours
- Dynamics of Chern-Simons vortices (David Stuart)
3 hours
Total time for lectures: 16 hours
Talks
- Andrew Comech,
Global attraction to solitary waves.
- Scipio Cuccagna,
On asymptotic stability of ground states of Nonlinear Schrödinger
Equations in energy space.
- Vladimir Georgiev,
Non-radial stability of solitary waves for Maxwell-Schrödinger system
with external potential.
- Markus Kunze,
Multipole radiation in a collisionless gas
coupled to electromagnetism.
- Lucattilio Tenuta, Quasi-static limits in nonrelativistic Quantum Electrodynamics.
Total time for talks: 5 hours
A list of participants
and their affiliation
- Vladimir Buslaev, buslaev@mph.phys.spbu.ru
Department of Mathematical and Computational Physics, Faculty of Physics, St. Petersburg University, St. Petersburg 198904, RUSSIA
- Andrew Comech, comech@math.tamu.edu
Institute for Information Transmission Problems, B. Karetnii 19, Moscow 101447, RUSSIA
- Scipio Cuccagna, cuccagna@unimo.it
DISMI, University of Modena and Reggio Emilia, Reggio Emilia 42100, ITALY
- Anton Dzhamay, adzham@unco.edu
School of Mathematical Sciences, University of Northern Colorado,
Greeley, CO 80639, USA
- Jan Derezinski, Jan.Derezinski@fuw.edu.pl
KMMF UW, Hoza 74, 00-682 Warszawa, POLAND
- Vladimir Georgiev, georgiev@dm.unipi.it
Dipartimento di Matematica, Universitá di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, ITALY
- Marcel Griesemer, Marcel.Griesemer@mathematik.uni-stuttgart.de
Universität Stuttgart, Fachbereich Mathematik, Institut für Analysis, Dynamik und Modellierung, Abteilung für Analysis, D-70569 Stuttgart, GERMANY
- Valery Imaikin, imaikin@ma.tum.de, ivm@infoline.su
Podlesnaja Street, 2-22, Town of Korolev
Moscow Region, 141080
RUSSIA
- Alexander Komech, alexander.komech@univie.ac.at
Zentrum Mathematik, Bereich M5, Technische Universität München, D-85747 Garching, GERMANY
- Elena Kopylova, ek@vpti.vladimir.ru
Institute for Information Transmission Problems, B. Karetnii 19, Moscow 101447, RUSSIA
- Evgeny Korotyaev, evgeny@math.hu-berlin.de
Institut fur Mathematik, Humboldt Universitat zu Berlin, Rudower Chaussee 25, D-12489 Berlin, GERMANY
- Markus Kunze, markus.kunze@uni-duisburg-essen.de
Universität Duisburg-Essen, Fachbereich Mathematik, D-45117 Essen, GERMANY
- Alexei Poltoratski, alexeip@math.tamu.edu
Department of Mathematics, Texas A&M University, College Station, TX 77843, USA
- Herbert Spohn, spohn@ma.tum.de
Zentrum Mathematik, Bereich M5, Technische Universität München, D-85747 Garching, GERMANY
- David Stuart, D.M.A.Stuart@damtp.cam.ac.uk
University of Cambridge, DAMTP-CMS, Wilberforce Road, Cambridge CB3 OWA, ENGLAND
- Lucattilio Tenuta, lucattilio.tenuta@uni-tuebingen.de
Mathematisches Institut, Eberhard-Karls-Universitaet, Auf der Morgenstelle 10, D-72076 Tuebingen, GERMANY
Abstract
The aim of the miniworkshop
is the discussion of the solitary wave asymptotics
for nonlinear Hamiltonian partial differential equations
and relation to mathematical problems of theoretical physics.
While the existence and orbital stability of solitary waves
is fairly well understood,
the asymptotic stability of solitary waves is still not understood
well.
The global attraction of arbitrary solutions of finite energy
to the set of solitary waves is not proved but in a few model cases.
On the other side, there is now accumulating a great number of recent results
that seem to enable us to make a crucial progress in this direction:
namely, to prove the solitary asymptotics for the -invariant
nonlinear Klein-Gordon equation
and similar dispersive Hamiltonian systems.
The research
is inspired by Bohr's postulate on
quantum transitions and
Schrödinger's identification
of the quantum stationary states to the nonlinear eigenfunctions
of the coupled -invariant
Maxwell-Schrödinger and Maxwell-Dirac equations.