From the hypergeometric differential equation to a non linear Schrödinger one

Abstract

We show that the q-exponential function is a hypergeometric function. Accordingly, it obeys the hypergeometric differential equation. We demonstrate that this differential equation is a non-linear Schrödinger equation (NLSE). This NLSE exhibits both similarities and differences vis-a-vis the Nobre-Rego Monteiro-Tsallis one.

11 pages, no figures. Text has changed. References added

References in corpus (2)

• Thermostatistics of overdamped motion of interacting particles
• Analysis of Self-Organized Criticality in the Olami-Feder-Christensen model and in real earthquakes

Cited by in corpus (6)

• q-Gamow States as continuous linear functionals on analytical test functions
• Hypergeometric Connotations of Quantum Equations
• Tsallis' Quantum q-Fields
• q-Gamow States for intermediate energies
• Lorentzian Solitary Wave in a Generalised Nonlinear Schrödinger Equation
• Hypergeometric foundations of Fokker-Plank like equations