Abstract:

We present a new, (transformation) group-theoretic approach to the classification of a class of Darboux integrable partial differential equations, commonly referred to as f-Gordon equations, generalized wave maps equations, or equations of Liouville type.
The main result of our approach asserts that a complete list of all f-Gordon equations which are Darboux integrable at order three can be determined from a complete list of all (real) 2-plane distributions in five dimensions which admit intransitive, 5-dimensional symmetry groups. Through this correspondence, we have uncovered a new class of f-Gordon equations, the addition of which completes the classification of f-Gordon equations Darboux integrable at order three. This talk is based upon joint work with Ian M. Anderson, Utah State University.