From the hypergeometric differential equation to a non-linear Schrödinger one

•We show that the q-exponential is a hypergeometric function.•It thus obeys the hypergeometric differential equation (HDE).•We show that the HDE can be cast as a non-linear Schrödinger equation.•This is different from the Nobre, Rego-Monteiro, Tsallis one.

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