Distribution of solitons from nonlinear integrable equations

A previous treatment that holds for the Kortewegde Vries equation is extended to cover the case of nonlinear integrable equations associated with the standard Zakharov-Shabat eigenvalue problem that has a complex discrete spectrum. Particularly, an analytical expression for the distribution function...

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Autores principales: Ponce Dawson, S., Ferro Fontn, C.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_10502947_v39_n10_p5289_PonceDawson
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_10502947_v39_n10_p5289_PonceDawson2023-10-03T15:58:49Z Distribution of solitons from nonlinear integrable equations Ponce Dawson, S. Ferro Fontn, C. A previous treatment that holds for the Kortewegde Vries equation is extended to cover the case of nonlinear integrable equations associated with the standard Zakharov-Shabat eigenvalue problem that has a complex discrete spectrum. Particularly, an analytical expression for the distribution function of solitons as a functional of the initial conditions is found. This distribution function gives the correct values of the infinite set of constants of motion and leads to a large number of conclusions that agree with previous numerical and analytical results. Special emphasis is given to a comparison of these results in the case of the derivative nonlinear Schrödinger equation. The distribution function is particularly useful for the statistical description of the nonlinear equations involved in the formalism (such as the nonlinear Schrödinger or the derivative nonlinear Schrödinger equations) when an ensemble of initial conditions is considered. © 1989 The American Physical Society. Fil:Ponce Dawson, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_10502947_v39_n10_p5289_PonceDawson
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description A previous treatment that holds for the Kortewegde Vries equation is extended to cover the case of nonlinear integrable equations associated with the standard Zakharov-Shabat eigenvalue problem that has a complex discrete spectrum. Particularly, an analytical expression for the distribution function of solitons as a functional of the initial conditions is found. This distribution function gives the correct values of the infinite set of constants of motion and leads to a large number of conclusions that agree with previous numerical and analytical results. Special emphasis is given to a comparison of these results in the case of the derivative nonlinear Schrödinger equation. The distribution function is particularly useful for the statistical description of the nonlinear equations involved in the formalism (such as the nonlinear Schrödinger or the derivative nonlinear Schrödinger equations) when an ensemble of initial conditions is considered. © 1989 The American Physical Society.
format JOUR
author Ponce Dawson, S.
Ferro Fontn, C.
spellingShingle Ponce Dawson, S.
Ferro Fontn, C.
Distribution of solitons from nonlinear integrable equations
author_facet Ponce Dawson, S.
Ferro Fontn, C.
author_sort Ponce Dawson, S.
title Distribution of solitons from nonlinear integrable equations
title_short Distribution of solitons from nonlinear integrable equations
title_full Distribution of solitons from nonlinear integrable equations
title_fullStr Distribution of solitons from nonlinear integrable equations
title_full_unstemmed Distribution of solitons from nonlinear integrable equations
title_sort distribution of solitons from nonlinear integrable equations
url http://hdl.handle.net/20.500.12110/paper_10502947_v39_n10_p5289_PonceDawson
work_keys_str_mv AT poncedawsons distributionofsolitonsfromnonlinearintegrableequations
AT ferrofontnc distributionofsolitonsfromnonlinearintegrableequations
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