Analytical properties and numerical solutions of the derivative nonlinear Schrödinger equation

From the analysis of the symmetries of the derivative nonlinear Schrodinger (DNLS) equation, we obtain a new constant of motion, which may be formally considered as a charge and which is related to the helicity of the physical system. From comparison of these symmetries and those of the soliton solu...

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Autor principal: Dawson, S.P.
Formato: JOUR
Materias:
Mathematical Techniques > Numerical Methods
System Stability > Lyapunov Methods
Schrodinger Equation
Solitons
Plasmas
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00223778_v40_n3_p585_Dawson
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00223778_v40_n3_p585_Dawson
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spelling todo:paper_00223778_v40_n3_p585_Dawson2023-10-03T14:32:31Z Analytical properties and numerical solutions of the derivative nonlinear Schrödinger equation Dawson, S.P. Mathematical Techniques--Numerical Methods System Stability--Lyapunov Methods Schrodinger Equation Solitons Plasmas From the analysis of the symmetries of the derivative nonlinear Schrodinger (DNLS) equation, we obtain a new constant of motion, which may be formally considered as a charge and which is related to the helicity of the physical system. From comparison of these symmetries and those of the soliton solutions, we draw conclusions about the number of constraints that must be imposed and the way a Liapunov functional must be constructed in order to study the solitons’ stability. We also examine the relationship between the stability with respect to form and the symmetries that are broken by the soliton solutions. We complete the analysis with some numerical simulations: we solve the DNLS equation taking a slightly perturbed soliton as an initial condition and study its temporal evolution, finding that, as expected, they are stable with respect to form. © 1988, Cambridge University Press. All rights reserved. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00223778_v40_n3_p585_Dawson
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Mathematical Techniques--Numerical Methods
System Stability--Lyapunov Methods
Schrodinger Equation
Solitons
Plasmas
spellingShingle Mathematical Techniques--Numerical Methods
System Stability--Lyapunov Methods
Schrodinger Equation
Solitons
Plasmas
Dawson, S.P.
Analytical properties and numerical solutions of the derivative nonlinear Schrödinger equation
topic_facet Mathematical Techniques--Numerical Methods
System Stability--Lyapunov Methods
Schrodinger Equation
Solitons
Plasmas
description From the analysis of the symmetries of the derivative nonlinear Schrodinger (DNLS) equation, we obtain a new constant of motion, which may be formally considered as a charge and which is related to the helicity of the physical system. From comparison of these symmetries and those of the soliton solutions, we draw conclusions about the number of constraints that must be imposed and the way a Liapunov functional must be constructed in order to study the solitons’ stability. We also examine the relationship between the stability with respect to form and the symmetries that are broken by the soliton solutions. We complete the analysis with some numerical simulations: we solve the DNLS equation taking a slightly perturbed soliton as an initial condition and study its temporal evolution, finding that, as expected, they are stable with respect to form. © 1988, Cambridge University Press. All rights reserved.
format JOUR
author Dawson, S.P.
author_facet Dawson, S.P.
author_sort Dawson, S.P.
title Analytical properties and numerical solutions of the derivative nonlinear Schrödinger equation
title_short Analytical properties and numerical solutions of the derivative nonlinear Schrödinger equation
title_full Analytical properties and numerical solutions of the derivative nonlinear Schrödinger equation
title_fullStr Analytical properties and numerical solutions of the derivative nonlinear Schrödinger equation
title_full_unstemmed Analytical properties and numerical solutions of the derivative nonlinear Schrödinger equation
title_sort analytical properties and numerical solutions of the derivative nonlinear schrödinger equation
url http://hdl.handle.net/20.500.12110/paper_00223778_v40_n3_p585_Dawson
work_keys_str_mv AT dawsonsp analyticalpropertiesandnumericalsolutionsofthederivativenonlinearschrodingerequation
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