## Monday July 25/3:30

MS11/Harbor 3

# Approximate Soliton Dynamics: Beyond Solitons as Particles

The inverse scattering transform (IST) provides a method for the exact solution of many nonlinear evolution equations. In addition, the IST method gives a framework for soliton perturbation theory in cases where the nonlinear evolution equation of interest is close, in some sense, to a member of the family of completely integrable equations.
In practice, however, the details of the IST method and soliton perturbation theory are often difficult enough that much of the dynamics of the evolution is unable to be completely determined. This is particularly the case when the interaction of dispersive radiation with the soliton is important, such as during the transient evolution of an initial condition into a soliton (or solitons) plus dispersive radiation.

In this regard, approximate methods that attempt to take into account the effect of this interaction on soliton evolution have recently been developed. Many of these methods are based on conservation laws and/or Lagrangians and variational equations. In this minisymposium, the speakers will present recent developments in the area of approximate methods for nonlinear evolution equations. They will also discuss examples from nonlinear wave motions, and applications from areas such as fluid mechanics (the KdV and mKdV equations) and nonlinear optics (the NLS equation).
**Organizers: William L. Kath, Northwestern University, and Noel F. Smyth, University of Edinburgh, Scotland**

*3:30: ***Radiation Damping for the Nonlinear Schrodinger Equation.** William L. Kath, Co-organizer
*4:00: ***Radiation and Soliton Evolution for the Korteweg-de Vries Equation.** William L. Kath, Co-organizer, and *Noel F. Smyth*, Co-organizer
*4:30: ***Title to be announced.** Speaker to be announced
*5:00: ***On the Number of Solitons for the Intermediate Long Wave Equation.** Touvia Miloh, University of Tel Aviv Israel, and* Antonmaria A. (Tim) Minzoni*, National Autonomous University of Mexico, Mexico City