Quasi-linear dynamics in nonlinear Schrödinger equation with periodic boundary conditions

M. Burak Erdoǧan; Vadim Zharnitsky

doi:10.1007/s00220-008-0454-0

Quasi-linear dynamics in nonlinear Schrödinger equation with periodic boundary conditions

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

Abstract

It is shown that a large subset of initial data with finite energy (L ² norm) evolves nearly linearly in nonlinear Schrödinger equation with periodic boundary conditions. These new solutions are not perturbations of the known ones such as solitons, semiclassical or weakly linear solutions.

Original language	English (US)
Pages (from-to)	655-673
Number of pages	19
Journal	Communications in Mathematical Physics
Volume	281
Issue number	3
DOIs	https://doi.org/10.1007/s00220-008-0454-0
State	Published - Aug 2008

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s00220-008-0454-0

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title = "Quasi-linear dynamics in nonlinear Schr{\"o}dinger equation with periodic boundary conditions",

abstract = "It is shown that a large subset of initial data with finite energy (L 2 norm) evolves nearly linearly in nonlinear Schr{\"o}dinger equation with periodic boundary conditions. These new solutions are not perturbations of the known ones such as solitons, semiclassical or weakly linear solutions.",

author = "Erdoǧan, {M. Burak} and Vadim Zharnitsky",

note = "Funding Information: The authors were partially supported by NSF grants DMS-0505216 (V. Z.) and DMS-0600101 (B. E.).",

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AU - Zharnitsky, Vadim

N1 - Funding Information: The authors were partially supported by NSF grants DMS-0505216 (V. Z.) and DMS-0600101 (B. E.).

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N2 - It is shown that a large subset of initial data with finite energy (L 2 norm) evolves nearly linearly in nonlinear Schrödinger equation with periodic boundary conditions. These new solutions are not perturbations of the known ones such as solitons, semiclassical or weakly linear solutions.

AB - It is shown that a large subset of initial data with finite energy (L 2 norm) evolves nearly linearly in nonlinear Schrödinger equation with periodic boundary conditions. These new solutions are not perturbations of the known ones such as solitons, semiclassical or weakly linear solutions.

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Quasi-linear dynamics in nonlinear Schrödinger equation with periodic boundary conditions

Abstract

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