On integrability of nonautonomous nonlinear schrödinger equations

Sergei Suslov

doi:10.1090/S0002-9939-2011-11176-6

On integrability of nonautonomous nonlinear schrödinger equations

Sergei Suslov

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

27 Scopus citations

Abstract

We show, in general, how to transform the nonautonomous nonlinear Schrödinger equation with quadratic Hamiltonians into the standard autonomous form that is completely integrable by the familiar inverse scattering method in nonlinear science. Derivation of the corresponding equivalent nonisospectral Lax pair is also outlined. A few simple integrable systems are discussed.

Original language	English (US)
Pages (from-to)	3067-3082
Number of pages	16
Journal	Proceedings of the American Mathematical Society
Volume	140
Issue number	9
DOIs	https://doi.org/10.1090/S0002-9939-2011-11176-6
State	Published - Sep 2012

Keywords

Completely integrable systems
Generalized harmonic oscillators
Green's function
Lax pair
Nonlinear Schrödinger equations
Propagator
Zakharov-Shabat system

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-2011-11176-6

Cite this

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abstract = "We show, in general, how to transform the nonautonomous nonlinear Schr{\"o}dinger equation with quadratic Hamiltonians into the standard autonomous form that is completely integrable by the familiar inverse scattering method in nonlinear science. Derivation of the corresponding equivalent nonisospectral Lax pair is also outlined. A few simple integrable systems are discussed.",

keywords = "Completely integrable systems, Generalized harmonic oscillators, Green's function, Lax pair, Nonlinear Schr{\"o}dinger equations, Propagator, Zakharov-Shabat system",

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AB - We show, in general, how to transform the nonautonomous nonlinear Schrödinger equation with quadratic Hamiltonians into the standard autonomous form that is completely integrable by the familiar inverse scattering method in nonlinear science. Derivation of the corresponding equivalent nonisospectral Lax pair is also outlined. A few simple integrable systems are discussed.

KW - Completely integrable systems

KW - Generalized harmonic oscillators

KW - Green's function

KW - Lax pair

KW - Nonlinear Schrödinger equations

KW - Propagator

KW - Zakharov-Shabat system

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ER -

On integrability of nonautonomous nonlinear schrödinger equations

Abstract

Keywords

ASJC Scopus subject areas

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