Uniqueness of standing-waves for a non-linear Schrodinger equation with three pure-power combinations in dimension one

Garrisi, D orcid.org/0000-0001-8999-3392 and Georgiev, V (2019) Uniqueness of standing-waves for a non-linear Schrodinger equation with three pure-power combinations in dimension one. In: Zheng, S, Beceanu, M, Bona, J, Chen, G, Van Phan, T and Soffer, A, (eds.) Nonlinear Dispersive Waves and Fluids: AMS Special Session on Spectral Calculus and Quasilinear Partial Differential Equations, and PDE Analysis on Fluid Flows. AMS-MAA Joint Mathematics Meetings, 725 . American Mathematical Society , p. 137. ISBN 978-1-4704-4109-8

Abstract

We show that symmetric and positive profiles of ground-state standing-wave of the non-linear Schrödinger equation are non-degenerate and unique up to a translation of the argument and multiplication by complex numbers in the unit sphere. The non-linear term is a combination of two or three pure- powers. The class of non-linearities satisfying the mentioned properties can be extended beyond two or three power combinations. Specifically, it is sufficient that an Euler differential inequality is satisfied and that a certain auxiliary function is such that the first local maximum is also an absolute maximum.

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Item Type:	Book Section
Authors/Creators:	Garrisi, D https://orcid.org/0000-0001-8999-3392 Georgiev, V
Editors:	Zheng, S Beceanu, M Bona, J Chen, G Van Phan, T Soffer, A
Dates:	Published: 12 March 2019 Accepted: 29 March 2018
Institution:	The University of Leeds
Academic Units:	The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds)
Depositing User:	Symplectic Publications
Date Deposited:	10 Apr 2018 09:58
Last Modified:	13 Aug 2019 09:08
Status:	Published
Publisher:	American Mathematical Society
Series Name:	AMS-MAA Joint Mathematics Meetings
Identification Number:	10.1090/conm/725
Open Archives Initiative ID (OAI ID):	oai:eprints.whiterose.ac.uk:129462

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Uniqueness of standing-waves for a non-linear Schrodinger equation with three pure-power combinations in dimension one

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