2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170593We provide a rigorous mathematical derivation of the convergence in the long-wave transonic limit of the minimizing travelling waves for the two-dimensional Gross-Pitaevskii equation towards ground states for the Kadomtsev-Petviashvili equation (KP I).Final version published in Dynamics of Partial Differential Equations, 5, 3, 2008, p. 241-280Analysis of PDEs35Q40, 35Q53, 35Q55text