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Quasi-stationary states of the NRT nonlinear Schrödinger equation. (English) Zbl 1395.81113
Summary: 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.

MSC:
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35Q55 NLS equations (nonlinear Schrödinger equations)
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