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 nonlinearities. Such systems are shown to perform periodic oscillations due to existing centers. We describe this system 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 system to a QES system. First few QES levels are calculated explicitly by using Bender–Dunne polynomial method. © 2020, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.