Transformation and factorization of partial differential systems

Abstract

Factorization of linear ordinary differential operators with variable coefficients is one of the well-known methods used for solution of the corresponding differential equations. Factorization of linear partial differential operators is a much more complicated problem. An appropriate modification of the naive definition of factorization gives rise to a bunch of new methods of closed-form solution of a single linear partial differential equation or a system of such equations. This approach is naturally related to differential transformations---another popular method of solution of differential equations.