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This paper systematically explores several kinds of PT-symmetric deformations of superderivatives, which include three types, namely (1) PT-symmetric superderivatives of bosonic-fermionic type, (2) PT-symmetric superderivatives of fermionic type and (3) PT-symmetric superderivatives of bosonic type. Based on these possible cases, we construct novel families of complex PT-symmetric extensions of three models, including the N=1 supersymmetric modified Korteweg-de Vries (mKdV) equation, the supersymmetric Ito’s equation and the supersymmetric KdV-Sawada-Kotera-Ramani equation. In addition, the non-Hermitian Hamiltonian deformations for the supersymmetric mKdV equation is considered. PT-symmetric deformation has established a new theoretical framework for non-Hermitian integrable models, expanding the fusion paradigm of supersymmetry and PT-symmetry.
Li et al. (Sun,) studied this question.