Examples of the investigation of differential equations with modularized programs (Q1368550)

The use of the REDUCE program CRACK for the symbolic integration and analysis of nonlinear differential equations is demonstrated on the basis of six examples: (i) determination of conservation laws of the Ito system and Fisher's equation, (ii) determination of the Lie symmetry algebra of a unified field theory, (iii) computing finite transformations from the infinitesimal symmetry generators of an ordinary differential equation stemming from general relativity, (iv) solving a quasi-linear partial differential equation arising in the normal form theory of vector fields, (v) solving the Killing equations of the Kimura metric, and (vi) finding a Lagrangian for the Painlevé VI equation.