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.
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