Rational solutions of Riccati-like partial differential equations

When factoring linear partial differential systems with a finite-dimensiona l solution space or analysing symmetries of nonlinear ODEs, we need to look for rational solutions of certain nonlinear PDEs. The nonlinear PDEs are c alled 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-lik e system, and an algorithm for computing them. The algorithm is also applic able to finding all rational solutions of Lie's system {partial derivative (x)u + u(2) + a(1)u + a(2)v + a(3), partial derivative (y)u + uv + b(1)u b(2)v + b(3), partial derivative (x)v + uv + c(1)v + c(2)v + c(3), partial derivative (y)v + v(2) + d(1)u + d(2)v + d(3)}, where a(1),..., d(3) are ra tional functions of x and y. (C) 2001 Academic Press.