Travelling waves for the Gross–Pitaevskii equation in dimension larger than two Original Research Article

We present a different approach than the one given in Bethuel et al. (J. Eur. Math. Soc. 6(1) (2004) 17) of the existence of travelling vortex rings solutions to the Gross–Pitaevskii equation in dimension N⩾3. We follow an idea, which was used before in Bethuel and Saut (Ann. IHP Phys. Theor. 70(2) (1999) 147) in dimension 2, invoking the mountain-pass lemma. It has the advantage of providing a full interval of propagation speeds (0,C0).