On modulated coupled systems. Canonical reduction via reciprocal transformations

Colin Rogers; Wolfgang K. Schief; Boris Malomed

doi:10.1016/j.cnsns.2019.105091

On modulated coupled systems. Canonical reduction via reciprocal transformations

Colin Rogers, Wolfgang K. Schief^*, Boris Malomed

^*Corresponding author for this work

School of Electrical Engineering

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

Abstract

It is shown how classes of modulated coupled systems of sine-Gordon, Demoulin and Manakov-type may be reduced to their unmodulated counterparts via the application of a novel reciprocal transformation. Modulations governed by recently introduced integrable Ermakov-Painlevé II, Ermakov-Painlevé III and Ermakov-Painlevé IV equations as well as the classical Ermakov equation are considered. In the latter case, the procedure is illustrated by the generation of a class of exact solutions to a heterogeneous Manakov system with periodic modulation.

Original language	English
Article number	105091
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	83
DOIs	https://doi.org/10.1016/j.cnsns.2019.105091
State	Published - Apr 2020

Keywords

Heterogeneous integrable system
Manakov system
Modulated soliton
Reciprocal transformation

Access to Document

10.1016/j.cnsns.2019.105091

Cite this

@article{ca4975d8a860429284d60675d3bb4caf,

title = "On modulated coupled systems. Canonical reduction via reciprocal transformations",

abstract = "It is shown how classes of modulated coupled systems of sine-Gordon, Demoulin and Manakov-type may be reduced to their unmodulated counterparts via the application of a novel reciprocal transformation. Modulations governed by recently introduced integrable Ermakov-Painlev{\'e} II, Ermakov-Painlev{\'e} III and Ermakov-Painlev{\'e} IV equations as well as the classical Ermakov equation are considered. In the latter case, the procedure is illustrated by the generation of a class of exact solutions to a heterogeneous Manakov system with periodic modulation.",

keywords = "Heterogeneous integrable system, Manakov system, Modulated soliton, Reciprocal transformation",

author = "Colin Rogers and Schief, {Wolfgang K.} and Boris Malomed",

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

year = "2020",

month = apr,

doi = "10.1016/j.cnsns.2019.105091",

language = "אנגלית",

volume = "83",

journal = "Communications in Nonlinear Science and Numerical Simulation",

issn = "1007-5704",

publisher = "Elsevier",

}

TY - JOUR

T1 - On modulated coupled systems. Canonical reduction via reciprocal transformations

AU - Rogers, Colin

AU - Schief, Wolfgang K.

AU - Malomed, Boris

PY - 2020/4

Y1 - 2020/4

N2 - It is shown how classes of modulated coupled systems of sine-Gordon, Demoulin and Manakov-type may be reduced to their unmodulated counterparts via the application of a novel reciprocal transformation. Modulations governed by recently introduced integrable Ermakov-Painlevé II, Ermakov-Painlevé III and Ermakov-Painlevé IV equations as well as the classical Ermakov equation are considered. In the latter case, the procedure is illustrated by the generation of a class of exact solutions to a heterogeneous Manakov system with periodic modulation.

AB - It is shown how classes of modulated coupled systems of sine-Gordon, Demoulin and Manakov-type may be reduced to their unmodulated counterparts via the application of a novel reciprocal transformation. Modulations governed by recently introduced integrable Ermakov-Painlevé II, Ermakov-Painlevé III and Ermakov-Painlevé IV equations as well as the classical Ermakov equation are considered. In the latter case, the procedure is illustrated by the generation of a class of exact solutions to a heterogeneous Manakov system with periodic modulation.

KW - Heterogeneous integrable system

KW - Manakov system

KW - Modulated soliton

KW - Reciprocal transformation

UR - http://www.scopus.com/inward/record.url?scp=85074922767&partnerID=8YFLogxK

U2 - 10.1016/j.cnsns.2019.105091

DO - 10.1016/j.cnsns.2019.105091

M3 - מאמר

AN - SCOPUS:85074922767

VL - 83

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

M1 - 105091

ER -

On modulated coupled systems. Canonical reduction via reciprocal transformations

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this