Kink–antikink stripe interactions in the two-dimensional sine–Gordon equation

R. Carretero-González; L.A. Cisneros-Ake; R. Decker; G.N. Koutsokostas; D.J. Frantzeskakis; P.G. Kevrekidis; D.J. Ratliff

doi:10.1016/j.cnsns.2021.106123

Kink–antikink stripe interactions in the two-dimensional sine–Gordon equation

R. Carretero-González^*, L.A. Cisneros-Ake, R. Decker, G.N. Koutsokostas, D.J. Frantzeskakis, P.G. Kevrekidis, D.J. Ratliff

^*Corresponding author for this work

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

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Abstract

The main focus of the present work is to study quasi-one-dimensional kink–antikink stripes embedded in the two-dimensional sine–Gordon equation. Using variational techniques, we reduce the interaction dynamics between a kink and an antikink stripe on their respective time and space dependent widths and locations. The resulting reduced system of coupled equations is found to accurately describe the width and undulation dynamics of a single kink stripe as well as that of two interacting ones. As an aside, we also discuss two related topics: the computational identification of the kink center and its numerical implications and alternative perturbative and multiple scales approaches to the transverse direction induced dynamics for a single kink stripe in the two-dimensional realm.

Original language	English
Article number	106123
Number of pages	24
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	109
Early online date	21 Feb 2022
DOIs	https://doi.org/10.1016/j.cnsns.2021.106123
Publication status	Published - 1 Jun 2022

Keywords

Sine–Gordon equation
Kink and anti-kinks
Kink stripes
Variational approximation

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10.1016/j.cnsns.2021.106123Licence: CC BY-NC-ND

1-s2.0-S1007570421004299-mainFinal published version, 5.63 MBLicence: CC BY-NC-ND

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title = "Kink–antikink stripe interactions in the two-dimensional sine–Gordon equation",

abstract = "The main focus of the present work is to study quasi-one-dimensional kink–antikink stripes embedded in the two-dimensional sine–Gordon equation. Using variational techniques, we reduce the interaction dynamics between a kink and an antikink stripe on their respective time and space dependent widths and locations. The resulting reduced system of coupled equations is found to accurately describe the width and undulation dynamics of a single kink stripe as well as that of two interacting ones. As an aside, we also discuss two related topics: the computational identification of the kink center and its numerical implications and alternative perturbative and multiple scales approaches to the transverse direction induced dynamics for a single kink stripe in the two-dimensional realm.",

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T1 - Kink–antikink stripe interactions in the two-dimensional sine–Gordon equation

AU - Carretero-González, R.

AU - Cisneros-Ake, L.A.

AU - Decker, R.

AU - Koutsokostas, G.N.

AU - Frantzeskakis, D.J.

AU - Kevrekidis, P.G.

AU - Ratliff, D.J.

PY - 2022/6/1

Y1 - 2022/6/1

N2 - The main focus of the present work is to study quasi-one-dimensional kink–antikink stripes embedded in the two-dimensional sine–Gordon equation. Using variational techniques, we reduce the interaction dynamics between a kink and an antikink stripe on their respective time and space dependent widths and locations. The resulting reduced system of coupled equations is found to accurately describe the width and undulation dynamics of a single kink stripe as well as that of two interacting ones. As an aside, we also discuss two related topics: the computational identification of the kink center and its numerical implications and alternative perturbative and multiple scales approaches to the transverse direction induced dynamics for a single kink stripe in the two-dimensional realm.

AB - The main focus of the present work is to study quasi-one-dimensional kink–antikink stripes embedded in the two-dimensional sine–Gordon equation. Using variational techniques, we reduce the interaction dynamics between a kink and an antikink stripe on their respective time and space dependent widths and locations. The resulting reduced system of coupled equations is found to accurately describe the width and undulation dynamics of a single kink stripe as well as that of two interacting ones. As an aside, we also discuss two related topics: the computational identification of the kink center and its numerical implications and alternative perturbative and multiple scales approaches to the transverse direction induced dynamics for a single kink stripe in the two-dimensional realm.

KW - Sine–Gordon equation

KW - Kink and anti-kinks

KW - Kink stripes

KW - Variational approximation

UR - https://www.scopus.com/pages/publications/85124882664

U2 - 10.1016/j.cnsns.2021.106123

DO - 10.1016/j.cnsns.2021.106123

M3 - Article

SN - 1007-5704

VL - 109

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

M1 - 106123

ER -

Kink–antikink stripe interactions in the two-dimensional sine–Gordon equation

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Keywords

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