QES solutions of a two-dimensional system with quadratic nonlinearities

Abstract: We consider a one parameter family of a PT symmetric two dimensional system with quadratic non-linearities. Such systems are shown to perform periodic oscillations due to existing centers. We describe this systems by constructing a non-Hermitian Hamiltonian of a particle with position dependent mass. We further construct a canonical transformation which maps this position dependent mass systems to a QES system. First few QES levels are calculated explicitly by using Bender-Dunne (BD) polynomial method.