In a previous paper , we investigated the asymptotic behaviour of subsonic travelling waves of finite energy for the Gross-Pitaevskii equation in every dimension $N \geq 2$. In particular, we gave their first-order asymptotics in case they were axisymmetric. In the present paper, we compute their first-order asymptotics at infinity in the general case.
"First order asymptotics for the travelling waves in the Gross-Pitaevskii equation." Adv. Differential Equations 11 (3) 259 - 280, 2006.