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Rarefaction pulses for the Nonlinear Schrödinger Equation in the transonic limit.

Abstract : We investigate the properties of finite energy travelling waves to the nonlinear Schrödinger 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. Béthuel, 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.
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https://hal.archives-ouvertes.fr/hal-00874591
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Submitted on : Friday, October 18, 2013 - 11:36:59 AM
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David Chiron, Mihai Maris. Rarefaction pulses for the Nonlinear Schrödinger Equation in the transonic limit.. Communications in Mathematical Physics, Springer Verlag, 2014, 326 (2), pp.329-392. ⟨hal-00874591⟩

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