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