Friday, June 5

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.

Organizer: Willy A. Hereman
Colorado School of Mines
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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MMD, 5/12/98