Friday, June 5

CM12
Symmetries, Conservation Laws, and Integrability of Wave Equations

10:15 AM-12:15 PM
Room 244
This session will run until 12:45 PM

To investigate the integrability of PDEs one can search for conserved densities, higher-order symmetries, or bi-Hamiltonian structures. Alternatively, one can analyze the singularity structure of solutions, or verify the Painleve property.

One of the speakers will address the integrability and special solutions of a ninth-order generalization of the classical Darboux-Halphen system. It will be shown that the general solution of the system has a complicated singularity structure involving movable natural barriers and dense branching.

The speakers in this minisymposium will discuss new techniques for the investigation of the integrability of nonlinear evolution and wave equations and novel methods to explicitly construct invariants and symmetries. They will present examples and discuss applications.

10:15 On the Classification of Integrable Systems

Jan A. Sanders, Free University Amsterdam, The Netherlands

10:45 Integrability, Invariants and Bi-Hamiltonian Structure of Vector Nonlinear Evolution Equations

Frank Verheest, University of Ghent, Belgium

11:15 Invariants and Symmetries for Partial Differential Equations and Lattices

Unal Goktas, Colorado School of Mines; and Willy Hereman, Organizer

11:45 The Darboux-Halphen System and the Singularity Structure of its Solutions

Mark J. Ablowitz, University of Colorado, Boulder; Sarbarish Chakravarty, University of New South Wales, Australia; and Rod Halburd, University of Colorado, Boulder

12:15 Finite-dimensional Hamiltonian Systems for Multiphase Solutions of the KP Equation

Bernard Deconinck, University of Colorado, Boulder

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