A generalized non-Hermitian oscillator Hamiltonian, N-fold supersymmetry   and position-dependent mass models
  A generalized non-Hermitian oscillator Hamiltonian is proposed that consists of additional linear terms which break PT-symmetry explicitly. The model is put into an equivalent Hermitian form by means of a similarity transformation and the criterion of N-fold supersymmetry with a position-dependent mass is shown to reside in it. 
Bijan Bagchi, Toshiaki Tanaka