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