The Zakharov–Shabat Spectral Problem for Complexification and Perturbation of the Korteweg–de Vries Equation

In this paper we consider examples of complex expansion (cKdV) and perturbation (pKdV) of the Korteweg–de Vries equation (KdV) and show that these equations have a representation in the form of the zero-curvature equation. In this case, we use the Lie algebra of 4-dimensional quadratic nilpotent mat...

Deskribapen osoa

Gorde:

Xehetasun bibliografikoak
Egile Nagusiak:	Redkina, T. V., Редькина, Т. В., Zakinyan, A. R., Закинян, А. Р., Zakinyan, R. G., Закинян, Р. Г.
Formatua:	Статья
Hizkuntza:	English
Argitaratua:	2023
Gaiak:	Complexification of the Korteweg–de Vries equation Zero-curvature equation Perturbations of the Korteweg–de Vries equation Conservation laws
Sarrera elektronikoa:	https://dspace.ncfu.ru/handle/20.500.12258/25453
Etiketak:	Etiketa erantsi Etiketarik gabe, Izan zaitez lehena erregistro honi etiketa jartzen!

id	ir-20.500.12258-25453
record_format	dspace
spelling	ir-20.500.12258-254532023-09-14T12:10:51Z The Zakharov–Shabat Spectral Problem for Complexification and Perturbation of the Korteweg–de Vries Equation Redkina, T. V. Редькина, Т. В. Zakinyan, A. R. Закинян, А. Р. Zakinyan, R. G. Закинян, Р. Г. Complexification of the Korteweg–de Vries equation Zero-curvature equation Perturbations of the Korteweg–de Vries equation Conservation laws In this paper we consider examples of complex expansion (cKdV) and perturbation (pKdV) of the Korteweg–de Vries equation (KdV) and show that these equations have a representation in the form of the zero-curvature equation. In this case, we use the Lie algebra of 4-dimensional quadratic nilpotent matrices. Moreover, it is shown that the simplest possible matrix representation of this algebra leads to the possibility of constructing a countable number of conservation laws for these equations. 2023-09-14T12:09:44Z 2023-09-14T12:09:44Z 2023 Статья Redkina, T.V., Zakinyan, A.R., Zakinyan, R.G. The Zakharov–Shabat Spectral Problem for Complexification and Perturbation of the Korteweg–de Vries Equation // Axioms. - 2023. - 12 (7), статья № 703. - DOI: 10.3390/axioms12070703 http://hdl.handle.net/20.500.12258/25453 en Axioms application/pdf application/pdf
institution	СКФУ
collection	Репозиторий
language	English
topic	Complexification of the Korteweg–de Vries equation Zero-curvature equation Perturbations of the Korteweg–de Vries equation Conservation laws
spellingShingle	Complexification of the Korteweg–de Vries equation Zero-curvature equation Perturbations of the Korteweg–de Vries equation Conservation laws Redkina, T. V. Редькина, Т. В. Zakinyan, A. R. Закинян, А. Р. Zakinyan, R. G. Закинян, Р. Г. The Zakharov–Shabat Spectral Problem for Complexification and Perturbation of the Korteweg–de Vries Equation
description	In this paper we consider examples of complex expansion (cKdV) and perturbation (pKdV) of the Korteweg–de Vries equation (KdV) and show that these equations have a representation in the form of the zero-curvature equation. In this case, we use the Lie algebra of 4-dimensional quadratic nilpotent matrices. Moreover, it is shown that the simplest possible matrix representation of this algebra leads to the possibility of constructing a countable number of conservation laws for these equations.
format	Статья
author	Redkina, T. V. Редькина, Т. В. Zakinyan, A. R. Закинян, А. Р. Zakinyan, R. G. Закинян, Р. Г.
author_facet	Redkina, T. V. Редькина, Т. В. Zakinyan, A. R. Закинян, А. Р. Zakinyan, R. G. Закинян, Р. Г.
author_sort	Redkina, T. V.
title	The Zakharov–Shabat Spectral Problem for Complexification and Perturbation of the Korteweg–de Vries Equation
title_short	The Zakharov–Shabat Spectral Problem for Complexification and Perturbation of the Korteweg–de Vries Equation
title_full	The Zakharov–Shabat Spectral Problem for Complexification and Perturbation of the Korteweg–de Vries Equation
title_fullStr	The Zakharov–Shabat Spectral Problem for Complexification and Perturbation of the Korteweg–de Vries Equation
title_full_unstemmed	The Zakharov–Shabat Spectral Problem for Complexification and Perturbation of the Korteweg–de Vries Equation
title_sort	zakharov–shabat spectral problem for complexification and perturbation of the korteweg–de vries equation
publishDate	2023
url	https://dspace.ncfu.ru/handle/20.500.12258/25453
work_keys_str_mv	AT redkinatv thezakharovshabatspectralproblemforcomplexificationandperturbationofthekortewegdevriesequation AT redʹkinatv thezakharovshabatspectralproblemforcomplexificationandperturbationofthekortewegdevriesequation AT zakinyanar thezakharovshabatspectralproblemforcomplexificationandperturbationofthekortewegdevriesequation AT zakinânar thezakharovshabatspectralproblemforcomplexificationandperturbationofthekortewegdevriesequation AT zakinyanrg thezakharovshabatspectralproblemforcomplexificationandperturbationofthekortewegdevriesequation AT zakinânrg thezakharovshabatspectralproblemforcomplexificationandperturbationofthekortewegdevriesequation AT redkinatv zakharovshabatspectralproblemforcomplexificationandperturbationofthekortewegdevriesequation AT redʹkinatv zakharovshabatspectralproblemforcomplexificationandperturbationofthekortewegdevriesequation AT zakinyanar zakharovshabatspectralproblemforcomplexificationandperturbationofthekortewegdevriesequation AT zakinânar zakharovshabatspectralproblemforcomplexificationandperturbationofthekortewegdevriesequation AT zakinyanrg zakharovshabatspectralproblemforcomplexificationandperturbationofthekortewegdevriesequation AT zakinânrg zakharovshabatspectralproblemforcomplexificationandperturbationofthekortewegdevriesequation
_version_	1809808699077689344

The Zakharov–Shabat Spectral Problem for Complexification and Perturbation of the Korteweg–de Vries Equation

Antzeko izenburuak