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


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

Wednesday afternoon: an excursion to the Black Forest to a restaurant - sturdy footwear is recommended.


Minicourses

  1. Asymptotic stability of solitary waves in nonlinear Schrödinger equation (Vladimir Buslaev) 4 hours
  2. Analytic Perturbation Theory and Renormalization Analysis of Matter coupled to quantized radiation (Marcel Griesemer) 3 hours
  3. Nonrelativistic QED: Anomalous magnetic moment (Herbert Spohn) 2 hours
  4. Scattering in nonrelativistic QFT (Jan Derezinski) 4 hours
  5. Dynamics of Chern-Simons vortices (David Stuart) 3 hours

Total time for lectures: 16 hours

Talks

  1. Andrew Comech, Global attraction to solitary waves.
  2. Scipio Cuccagna, On asymptotic stability of ground states of Nonlinear Schrödinger Equations in energy space.
  3. Vladimir Georgiev, Non-radial stability of solitary waves for Maxwell-Schrödinger system with external potential.
  4. Markus Kunze, Multipole radiation in a collisionless gas coupled to electromagnetism.
  5. Lucattilio Tenuta, Quasi-static limits in nonrelativistic Quantum Electrodynamics.

Total time for talks: 5 hours


A list of participants and their affiliation


  1. Vladimir Buslaev, buslaev@mph.phys.spbu.ru
    Department of Mathematical and Computational Physics, Faculty of Physics, St. Petersburg University, St. Petersburg 198904, RUSSIA

  2. Andrew Comech, comech@math.tamu.edu
    Institute for Information Transmission Problems, B. Karetnii 19, Moscow 101447, RUSSIA

  3. Scipio Cuccagna, cuccagna@unimo.it
    DISMI, University of Modena and Reggio Emilia, Reggio Emilia 42100, ITALY

  4. Anton Dzhamay, adzham@unco.edu
    School of Mathematical Sciences, University of Northern Colorado, Greeley, CO 80639, USA

  5. Jan Derezinski, Jan.Derezinski@fuw.edu.pl
    KMMF UW, Hoza 74, 00-682 Warszawa, POLAND

  6. Vladimir Georgiev, georgiev@dm.unipi.it
    Dipartimento di Matematica, Universitá di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, ITALY

  7. 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

  8. Valery Imaikin, imaikin@ma.tum.de, ivm@infoline.su
    Podlesnaja Street, 2-22, Town of Korolev Moscow Region, 141080 RUSSIA

  9. Alexander Komech, alexander.komech@univie.ac.at
    Zentrum Mathematik, Bereich M5, Technische Universität München, D-85747 Garching, GERMANY

  10. Elena Kopylova, ek@vpti.vladimir.ru
    Institute for Information Transmission Problems, B. Karetnii 19, Moscow 101447, RUSSIA

  11. Evgeny Korotyaev, evgeny@math.hu-berlin.de
    Institut fur Mathematik, Humboldt Universitat zu Berlin, Rudower Chaussee 25, D-12489 Berlin, GERMANY

  12. Markus Kunze, markus.kunze@uni-duisburg-essen.de
    Universität Duisburg-Essen, Fachbereich Mathematik, D-45117 Essen, GERMANY

  13. Alexei Poltoratski, alexeip@math.tamu.edu
    Department of Mathematics, Texas A&M University, College Station, TX 77843, USA

  14. Herbert Spohn, spohn@ma.tum.de
    Zentrum Mathematik, Bereich M5, Technische Universität München, D-85747 Garching, GERMANY

  15. David Stuart, D.M.A.Stuart@damtp.cam.ac.uk
    University of Cambridge, DAMTP-CMS, Wilberforce Road, Cambridge CB3 OWA, ENGLAND

  16. 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 $\mathbf{U}(1)$-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 $\mathbf{U}(1)$-invariant Maxwell-Schrödinger and Maxwell-Dirac equations.