Group Theory and exact Solutions of Partially Integrable Differential Systems

Abstract

The application of Lie group theory to obtain exact analytic solutions of nonlinear differential equations is reviewed. The emphasis is on recent developments such as the use of infinite dimensional symmetry groups, on algorithms for classifying finite dimensional subgroups of both finite and infinite dimensional Lie groups and on the combination of Lie group theory with singularity analysis (Painleve analysis). At each stage the use of computer algebra plays an important role: for finding the symmetry group, for identifying its Lie algebra, classifying its subgroups and performing Painleve analysis.