The computation of quasi-periodic solutions of integrable partial differential equationss

Bernard Deconinck

Abstract: Many integrable differential equations have periodic or quasiperiodic
solutions that are expressed in terms of multiphase Riemann theta
functions. The nature in which these solutions are effectively
parametrized by a compact, connected Riemann surface is a significant
obstacle to their computation and thus to their applicability. To overcome
these obstructions, a collection of black-box programs has been developed
in Maple. The ultimate goal of this ongoing effort is to significantly
improve the accessibility of these solutions.
A discussion of these solutions will be presented, followed by a
demonstration of the Maple programs.