Symplectic nonsqueezing in Hilbert space and discrete Schrödinger equations

Alexandre Sukhov, Alexander Tumanov

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)867-888
Number of pages22
JournalJournal of Fixed Point Theory and Applications
Volume18
Issue number4
DOIs
StatePublished - Dec 1 2016

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Hilbert spaces
Discrete Equations
Hilbert space
Curve Complex
Nonlinear equations
Nonlinear Equations
Theorem
Generalization

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

Cite this

Symplectic nonsqueezing in Hilbert space and discrete Schrödinger equations. / Sukhov, Alexandre; Tumanov, Alexander.

In: Journal of Fixed Point Theory and Applications, Vol. 18, No. 4, 01.12.2016, p. 867-888.

Research output: Contribution to journalArticle

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