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

Daniele Garrisi, Vladimir Georgiev

Research output: Chapter in Book/Conference proceedingConference contributionpeer-review

Abstract

We show that symmetric and positive profiles of ground-state standing-wave of the non-linear Schr¨odinger 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.
Original languageEnglish
Title of host publicationNonlinear dispersive waves and fluids
Subtitle of host publicationAMS Special Session on Spectral Calculus and Quasilinear Partial Differential Equations, and PDE Analysis on Fluid Flows, January 5-6, 2017, Atlanta, Georgia
EditorsShijun Zheng, Marius Beceanu, J. L. Bona, Geng Chen, Tuoc Phan, Avy Soffer
PublisherAmerican Mathematical Society
Pages137-148
Number of pages12
ISBN (Print)9781470441098
Publication statusPublished - 2019
EventAMS Special Sessions on Spectral Calculus
and Quasilinear Partial Differential Equations,
and PDE Analysis on Fluid Flows
- Atlanta, Georgia, United States
Duration: 5 Jan 20177 Jan 2017

Publication series

NameContemporary mathematics
Volume725

Conference

ConferenceAMS Special Sessions on Spectral Calculus
and Quasilinear Partial Differential Equations,
and PDE Analysis on Fluid Flows
Country/TerritoryUnited States
CityAtlanta, Georgia
Period5/01/177/01/17

Keywords

  • Wave equation
  • Nonlinear waves
  • Nonlinear wave equations

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