Douglas Baldwin

MACS Senior Seminar II D

Seminar date: 17 January 2003

ABSTRACT

A new algorithm for symbolic computation

A new algorithm for the symbolic computation of polynomial recursion
operators for systems of nonlinear evolution equations is presented.
The existence of a recursion operator assures the integrability of the
system.
The algorithm is implemented in Mathematica.
The software package automatically carries out the lengthy symbolic
computations for the construction and testing of recursion operators.
For systems with constant parameters, the software finds the conditions on
the parameters so that the given differential equations admit a recursion
operator.
The code is tested on several well-known partial differential equations from
soliton theory.