Symplectic nonsqueezing in Hilbert space and discrete Schrödinger equations

Alexandre Sukhov; Alexander Tumanov

doi:10.1007/s11784-016-0318-8

Symplectic nonsqueezing in Hilbert space and discrete Schrödinger equations

Alexandre Sukhov, Alexander Tumanov

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove a generalization of Gromov’s symplectic nonsqueezing theorem for the case of Hilbert spaces. Our approach is based on filling almost complex Hilbert spaces by complex discs partially extending Gromov’s results on existence of J-complex curves. We apply our result to the flow of the discrete nonlinear Schrödinger equation.

Original language	English (US)
Pages (from-to)	867-888
Number of pages	22
Journal	Journal of Fixed Point Theory and Applications
Volume	18
Issue number	4
DOIs	https://doi.org/10.1007/s11784-016-0318-8
State	Published - Dec 1 2016

Keywords

Hamiltonian PDE
Hilbert space
J-complex disc
Symplectic diffeomorphism
almost complex structure
discrete nonlinear Schrödinger equation

ASJC Scopus subject areas

Modeling and Simulation
Geometry and Topology
Applied Mathematics

Online availability

10.1007/s11784-016-0318-8

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abstract = "We prove a generalization of Gromov{\textquoteright}s symplectic nonsqueezing theorem for the case of Hilbert spaces. Our approach is based on filling almost complex Hilbert spaces by complex discs partially extending Gromov{\textquoteright}s results on existence of J-complex curves. We apply our result to the flow of the discrete nonlinear Schr{\"o}dinger equation.",

keywords = "Hamiltonian PDE, Hilbert space, J-complex disc, Symplectic diffeomorphism, almost complex structure, discrete nonlinear Schr{\"o}dinger equation",

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AU - Tumanov, Alexander

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AB - We prove a generalization of Gromov’s symplectic nonsqueezing theorem for the case of Hilbert spaces. Our approach is based on filling almost complex Hilbert spaces by complex discs partially extending Gromov’s results on existence of J-complex curves. We apply our result to the flow of the discrete nonlinear Schrödinger equation.

KW - Hamiltonian PDE

KW - Hilbert space

KW - J-complex disc

KW - Symplectic diffeomorphism

KW - almost complex structure

KW - discrete nonlinear Schrödinger equation

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ER -

Symplectic nonsqueezing in Hilbert space and discrete Schrödinger equations

Abstract

Keywords

ASJC Scopus subject areas

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