Symplectic Non-Squeezing for the Cubic NLS on the Line

Rowan Killip, Monica Vişan, Xiaoyi Zhang

Type: Article

Publication Date: 2017-07-10

Citations: 3

DOI: https://doi.org/10.1093/imrn/rnx152

Abstract

We prove symplectic non-squeezing for the cubic nonlinear Schrödinger equation on the line via finite-dimensional approximation.

Locations

International Mathematics Research Notices - View - PDF
arXiv (Cornell University) - View - PDF

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+ PDF Chat	Well-posedness issues on the periodic modified Kawahara equation	2019	Chulkwang Kwak
+ PDF Chat	Symplectic nonsqueezing for the KdV flow on the line	2022	Maria Ntekoume
+ PDF Chat	Nonlinear Evolution Equations: Analysis and Numerics	2020	Marlis Hochbruck Herbert Koch Sung‐Jin Oh Alexander Ostermann

Works Cited by This (20)

Action	Title	Year	Authors
+ PDF Chat	Global well-posedness and scattering for the defocusing, $L^{2}$-critical nonlinear Schrödinger equation when $d ≥3$	2011	Benjamin Dodson
+	Symplectic non-squeezing for the cubic nonlinear Klein-Gordon equation on $\mathbb{T}^3$	2014	Dana Mendelson
+	Sur les ensembles compacts de fonctions sommables	1988	Marcel Riesz
+ PDF Chat	Infinite-dimensional symplectic capacities and a squeezing theorem for Hamiltonian PDE's	1995	Sergej B. Kuksin
+ PDF Chat	Symplectic nonsqueezing of the korteweg-de vries flow	2005	J. Colliander Gigliola Staffilani M. Keel Hideo Takaoka Terence Tao
+	Pseudo holomorphic curves in symplectic manifolds	1985	M. Gromov
+	Asymptotically-Free Solutions for the Short-Range Nonlinear Schrödinger Equation	2001	Kenji Nakanishi
+ PDF Chat	Aspects of Long Time Behaviour of Solutions of Nonlinear Hamiltonian Evolution Equations	1995	Jean Bourgain
+	High frequency approximation of solutions to critical nonlinear wave equations	1999	Hajer Bahouri Patrick Gérard
+	Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations	1993	Jean Bourgain