arXiv:1210.1315 Abstract | arXiv Analytics

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Rarefaction pulses for the Nonlinear Schrodinger Equation in the transonic limit

Published 2012-10-04Version 1

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.

Comments: 48 pages

Categories: math.AP

Subjects: 35C07, 35B40, 35Q55, 35Q53

Keywords: nonlinear schrodinger equation, transonic limit, rarefaction pulses, two-dimensional gross-pitaevskii equation, finite energy travelling waves

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