Projektseminar (Functional Analysis): Stability of Nonlinear Waves
Wintersemester 2016/17

Time and Place
Type: Time: Place: Start:
SE 2 std. Tue 10:15-11:45 SR12 4.10
The stability of linear and nonlinear waves has a fascinating history. In this seminar we would like to discuss basic approaches to the problem of stability (spectral, orbital and asymptotic) of solitary waves. Our main aim is to look at a circle of ideas and the mathematical machinery that has been built to investigate the stability problem.
Date: Title: Speaker: References:
08.11Travelling Wave solutionsGerald Teschl[Pava] Chapter 3
15.11Scalar viscous conservation laws or NLS-type equations IMarkus Sobotnik[K-P] Sect 4.4 or 4.5
22.11Scalar viscous conservation laws or NLS-type equations IIMarkus Sobotnik[K-P] Sect 4.4 or 4.5
29.11The gKdV equations IMarkus Holzleitner[K-P] Sect 5.2.1
13.12The gKdV equations IIMarkus Holzleitner[K-P] Sect 5.2.1
17.01General Orbital Stability (+Exercises)Noema Nicolussi[K-P] Sect 5.2.2
24.01Eigenvalues of Constrained Self-Adjoint OperatorsLeopold Veselka[K-P] Sect 5.3


  1. M. Grillakis, J. Shatah and W. Strauss, Stability theory of solitary waves in the presence of symmetry. I, J. Funct. Anal. 74, 160-197 (1987); II, 94, 308-348 (1990).
  2. T. Kapitula and K. Promislow, Spectral and Dynamical Stability of Nonlinear Waves, Springer, New York, 2013.
  3. J. A. Pava, Nonlinear Dispersive Equations: Existence and Stability of Solitary and Periodic Travelling Wave Solutions, Amer. Math. Soc., Providence, 2009.
  4. A. Soffer and M. I. Weinstein, Multichannel nonlinear scattering for nonintegrable equations. Commun. Math. Phys. 133, 119-146 (1990).
  5. A. Soffer and M. I. Weinstein, Resonances, radiation damping and instability in Hamiltonian nonlinear wave equations. Invent. Math. 136, 9-74 (1999).
Course assessment
Preparation and presentation of a chosen topic. Active participation during the seminar.
Majors in Mathematics (master program, code MANS), Physics, ...
Auf Ihr Kommen freuen sich Aleksey Kostenko und Gerald Teschl