Quasi-stationary states of the NRT nonlinear Schrödinger equation

With regards to the nonlinear Schrödinger equation recently advanced by Nobre, Rego-Monteiro, and Tsallis (NRT), based on Tsallis q-thermo-statistical formalism, we investigate the existence and properties of its quasi-stationary solutions, which have the time and space dependences “separated” in a q-deformed fashion. One recovers the normal factorization into purely spatial and purely temporal factors, corresponding to the standard, linear Schrödinger equation, when the deformation vanishes (q=1). We discuss various specific examples of exact, quasi-stationary solutions of the NRT equation. In particular, we obtain a quasi-stationary solution for the Moshinsky model, providing the first example of an exact solution of the NRT equation for a system of interacting particles. •We explore quasi-stationary solutions of a nonlinear Schrödinger equation based upon the non-extensive thermostatistics.•We show that the NRT equation with quadratic potentials admits q-Gaussian quasi-stationary solutions.•We obtain an exact quasi-stationary solution for the Moshinsky model.