attention to the Pöschl-Teller (PT) potential, which has been applied to model various situations in recent years [@tong1; @tong2; @indjin; @tomak1; @tomak2]. In fact, the PT potential has been used in the context of deep quantum wells, as well as for modeling optical systems with changing refractive index. The PT potential depends upon two parameters and by varying them one can switch from a symmetric to an asymmetric situation. Yildirim and Tomak studied in particular the nonlinear optical properties associated to the PT potential [@tomak1], and also the nonlinear changes in the refractive index resulting from its tunable asymmetry [@tomak2].

Another important feature of the PT potential is that it is exactly solvable and characterized by a quadratic spectrum: as a consequence its time evolution shows fractional revivals [@averbukh; @robinett] and it may lead to the generation of linear superpositions of well distinct states in phase space. In this paper we confirm this expectation and find that an initial coherent state of the PT potential shows sub-Planck structures in phase-space at fractional revival times. We shall first study these structures when the PT potential is symmetric and then, by tuning the potential parameters, we switch to the asymmetric case in 