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Nonlinear coherent states (CSs) and their {\it dual families} were introducedrecently. In this paper we want to obtain their superposition and investigatetheir non-classical properties such as antibunching effect, quadraturesqueezing and amplitude squared squeezing. For this purpose two types ofsuperposition are considered. In the first type we neglect the normalizationfactors of the two components of the dual pair, superpose them and then wenormalize the obtained states, while in the second type we superpose the twonormalized components and then again normalize the resultant states. As aphysical realization, the formalism will then be applied to a special physicalsystem with known nonlinearity function, i.e., Hydrogen-like spectrum. Wecontinue with the (first type of) superposition of the dual pair ofGazeau-Klauder coherent states (GKCSs) as temporally stable CSs. An applicationof the proposal will be given by employing the P\"oschl-Teller potentialsystem. The numerical results are presented and discussed in detail, showingthe effects of this special quantum interference.

Superpositions of the dual family of nonlinear coherent states and their non-classical properties