Rational solutions of Riccati-like Partial Differential Equations

摘要

When factoring linear partial differential systems with a finite-dimensional solution space or analysing symmetries of nonlinear ODEs, we need to look for rational solutions of certain nonlinear PDEs. The nonlinear PDEs are called Riccati - like because they arise in a similar way as Riccati ODEs. In this paper we describe the structure of rational solutions of a Riccati - like system, and an algorithm for computing them.