Computing the Abel Transform
by
Bernard Deconinck
University of Washington

All integrable equations have large classes of (quasi)periodic solutions that are expressed in terms of Riemann theta functions. These solutions are parametrized in terms of Riemann surfaces. This parametrization is highly transcendental, obstructing the accessibility of these solutions. Previous efforts have reduced the computation of Riemann theta functions and some parts of this parametrization to black-box programs. In this talk, I will describe an algorithm for the implementation of the Abel transform, allowing for the (maple) computation of the phases of the (quasi)periodic solution.

Date received: October 7, 2003