On the KP I transonic limit of two-dimensional Gross-Pitaevskii travelling waves
Fabrice B\'ethuel (LJLL), Philippe Gravejat (CEREMADE), Jean-Claude, Saut (LM-Orsay)
TL;DR
This paper rigorously proves that in the transonic limit, traveling wave solutions of the 2D Gross-Pitaevskii equation converge to ground states of the KP I equation, linking quantum fluid models to integrable PDEs.
Contribution
It provides a rigorous mathematical derivation of the convergence from Gross-Pitaevskii traveling waves to KP I ground states in the transonic limit.
Findings
Convergence of traveling waves to KP I ground states in the transonic limit
Mathematical link between Gross-Pitaevskii and KP I equations
Rigorous proof of long-wave limit behavior
Abstract
We 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).
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Taxonomy
TopicsNonlinear Photonic Systems · Advanced Mathematical Physics Problems · Nonlinear Dynamics and Pattern Formation