Pilot wave approach to the NRT nonlinear Schrödinger equation

We investigate the main features of a pilot wave representation of the nonlinear Schrödinger equation recently advanced by Nobre, Rego-Monteiro, and Tsallis (NRT) on the basis of Tsallis q-thermo-statistical formalism. The present approach sheds new light upon the NRT equation. In particular, it suggests a new point of view concerning an apparent inconsistency concerning the physical meaning of its q-plane wave solutions. •We develop the pilot wave representation of a non-linear Schrödinger equation based on the non-extensive thermostatistics.•We study in detail the pilot wave model associated with exact solutions of the NRT equation.•We show that for q-plane wave solutions of the Bohmian velocity field is q-invariant.