International Conference: Nonlinear Waves--Theory and Applications


Periodic Problems in Soliton Equations

Annalisa Calini and Stéphane Lafortune

Department of Mathematics, College of Charleston, USA

This minisymposium brings together researchers whose work addresses diverse aspects of soliton equations with periodic boundary conditions. The periodic problem of completely integrable nonlinear PDEs is a both rich and challenging area of study, which brings together techniques and results from algebraic geometry and functional analysis, spectral theory and perturbation methods. The proposed minisymposium will discuss both theoretical and applied aspects, including construction and analysis of special solutions, spectral stability analysis of periodic solutions, issues of algebraic complete integrability in the algebro-geometric context, universal aspects of small dispersion limits, and applications of periodic theory to vortex filament dynamics and to rogue waves generation in deep water. 

Speakers List (in alphabetical order of authors):

1. Annalisa Calini (College of Charleston Charleston, USA)
Cable Formation for Finite-Gap Solutions of the Vortex Filament Flow
   Co-author: Tom Ivey (College of Charleston)

2. John Carter (Seattle University, USA)
    Stability of plane-wave solutions to a dissipative generalization of the
vector NLS equation

3. Bernard Deconinck (University of Washington, USA)
    KdV cnoidal waves are linearly stable.

4. Thomas Ivey (College of Charleston Charleston, USA)
    Finite-Gap Solutions of the Vortex Filament Flow: Genus One Solutions and Symmetric Solutions

5. Stéphane Lafortune (College of Charleston Charleston, USA)
   Stability Analysis of Persisting Periodic Solutions to
a Complex Ginzburg-Landau Perturbation of NLS
   Co-author: Tom Ivey (College of Charleston)