2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/218796The purpose of this paper is to provide a rigorous mathematical proof of the existence of travelling wave solutions to the Gross-Pitaevskii equation in dimensions two and three. Our arguments, based on minimization under constraints, yield a full branch of solutions, and extend earlier results, where only a part of the branch was built. In dimension three, we also show that there are no travelling wave solutions of small energy.Final version accepted for publication in Communications in Mathematical Physics with a few minor corrections and added remarksAnalysis of PDEs35Q55, 35Q51text