Rarefaction pulses for the Nonlinear Schrodinger Equation in the transonic limit
Analysis of PDEs
2012-10-05 v1
Abstract
We investigate the properties of finite energy travelling waves to the nonlinear Schrodinger equation with nonzero conditions at infinity for a wide class of nonlinearities. In space dimension two and three we prove that travelling waves converge in the transonic limit (up to rescaling) to ground states of the Kadomtsev-Petviashvili equation. Our results generalize an earlier result of F. Bethuel, P. Gravejat and J-C. Saut for the two-dimensional Gross-Pitaevskii equation, and provide a rigorous proof to a conjecture by C. Jones and P. H. Roberts about the existence of an upper branch of travelling waves in dimension three.
Keywords
Cite
@article{arxiv.1210.1315,
title = {Rarefaction pulses for the Nonlinear Schrodinger Equation in the transonic limit},
author = {David Chiron and Mihai Maris},
journal= {arXiv preprint arXiv:1210.1315},
year = {2012}
}
Comments
48 pages