Spectral problem for a two-component nonlinear Schrödinger equation in 2+1 dimensions: Singular manifold method and Lie point symmetries

P. Albares; J. M. Conde; P. G. Estévez

doi:10.1016/j.amc.2019.03.013

Spectral problem for a two-component nonlinear Schrödinger equation in 2+1 dimensions: Singular manifold method and Lie point symmetries

P. Albares
, J. M. Conde
, P. G. Estévez^*

^*Corresponding author for this work

Universidad San Francisco de Quito USFQ

Universidad de Salamanca

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

10 Scopus citations

Abstract

An integrable two-component nonlinear Schrödinger equation in 2+1 dimensions is presented. The singular manifold method is applied in order to obtain a three-component Lax pair. The Lie point symmetries of this Lax pair are calculated in terms of nine arbitrary functions and one arbitrary constant that yield a non-trivial infinite-dimensional Lie algebra. The main non-trivial similarity reductions associated to these symmetries are identified. The spectral parameter of the reduced spectral problem appears as a consequence of one of the symmetries.

Original language	English
Pages (from-to)	585-594
Number of pages	10
Journal	Applied Mathematics and Computation
Volume	355
DOIs	https://doi.org/10.1016/j.amc.2019.03.013
State	Published - 15 Aug 2019

Keywords

Integrability
Lax pair
Lie symmetries
Nonlinear Schrödinger equation
Painleve property
Similarity reductions

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10.1016/j.amc.2019.03.013

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@article{069c8ba0536b4596bf224876c4ca7f53,

title = "Spectral problem for a two-component nonlinear Schr{\"o}dinger equation in 2+1 dimensions: Singular manifold method and Lie point symmetries",

abstract = "An integrable two-component nonlinear Schr{\"o}dinger equation in 2+1 dimensions is presented. The singular manifold method is applied in order to obtain a three-component Lax pair. The Lie point symmetries of this Lax pair are calculated in terms of nine arbitrary functions and one arbitrary constant that yield a non-trivial infinite-dimensional Lie algebra. The main non-trivial similarity reductions associated to these symmetries are identified. The spectral parameter of the reduced spectral problem appears as a consequence of one of the symmetries.",

keywords = "Integrability, Lax pair, Lie symmetries, Nonlinear Schr{\"o}dinger equation, Painleve property, Similarity reductions",

author = "P. Albares and Conde, \{J. M.\} and Est{\'e}vez, \{P. G.\}",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2019",

month = aug,

day = "15",

doi = "10.1016/j.amc.2019.03.013",

language = "Ingl{\'e}s",

volume = "355",

pages = "585--594",

journal = "Applied Mathematics and Computation",

issn = "0096-3003",

publisher = "Elsevier Inc.",

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TY - JOUR

T1 - Spectral problem for a two-component nonlinear Schrödinger equation in 2+1 dimensions

T2 - Singular manifold method and Lie point symmetries

AU - Albares, P.

AU - Conde, J. M.

AU - Estévez, P. G.

PY - 2019/8/15

Y1 - 2019/8/15

N2 - An integrable two-component nonlinear Schrödinger equation in 2+1 dimensions is presented. The singular manifold method is applied in order to obtain a three-component Lax pair. The Lie point symmetries of this Lax pair are calculated in terms of nine arbitrary functions and one arbitrary constant that yield a non-trivial infinite-dimensional Lie algebra. The main non-trivial similarity reductions associated to these symmetries are identified. The spectral parameter of the reduced spectral problem appears as a consequence of one of the symmetries.

AB - An integrable two-component nonlinear Schrödinger equation in 2+1 dimensions is presented. The singular manifold method is applied in order to obtain a three-component Lax pair. The Lie point symmetries of this Lax pair are calculated in terms of nine arbitrary functions and one arbitrary constant that yield a non-trivial infinite-dimensional Lie algebra. The main non-trivial similarity reductions associated to these symmetries are identified. The spectral parameter of the reduced spectral problem appears as a consequence of one of the symmetries.

KW - Integrability

KW - Lax pair

KW - Lie symmetries

KW - Nonlinear Schrödinger equation

KW - Painleve property

KW - Similarity reductions

UR - https://www.scopus.com/pages/publications/85063319424

U2 - 10.1016/j.amc.2019.03.013

DO - 10.1016/j.amc.2019.03.013

M3 - Artículo

AN - SCOPUS:85063319424

SN - 0096-3003

VL - 355

SP - 585

EP - 594

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

Spectral problem for a two-component nonlinear Schrödinger equation in 2+1 dimensions: Singular manifold method and Lie point symmetries

Abstract

Keywords

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