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We systematically construct a distinct class of complex potentials includingparity-time ($\cal PT$) symmetric potentials for the stationary Schr\"odingerequation by using the soliton and periodic solutions of the four integrablereal nonlinear evolution equations (NLEEs) namely the sine-Gordon (sG)equation, the modified Korteweg-de Vries (mKdV) equation, combined mKdV-sGequation and the Gardner equation. These potentials comprise of kink, breather,bion, elliptic bion, periodic and soliton potentials which are explicitlyconstructed from the various respective solutions of the NLEEs. We demonstratethe relevance between the identified complex potentials and the potential ofthe graphene model from an application point of view.

journal of physics. a, mathematical and theoretical

A systematic construction of parity-time ($\cal PT$)-symmetric and  non-$\cal PT$-symmetric complex potentials from the solutions of various real  nonlinear evolution equations