Self-similarity analysis of the non-linear Schrödinger equation in the Madelung form

Imre F. Barna, Mihály A. Pocsai, L. Mátyás

In the present study a particular case of Gross-Pitaevskii or non-linear Schrödinger equation is rewritten to a form similar to a hydrodynamic Euler equation using the Madelung tra…