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The Existence of Heteroclinic Travelling Waves in the Discrete Sine-Gordon Equation with Nonlinear Interaction on a 2D-Lattice

The Existence of Heteroclinic Travelling Waves in the Discrete Sine-Gordon Equation with Nonlinear Interaction on a 2D-Lattice

The article deals with the discrete sine-Gordon equation that describes an infinite system of nonlinearly coupled nonlinear oscillators on a 2D-lattice with the external potential V (r) = K(1 - cos r). The main result concerns the existence of heteroclinic travelling waves solutions. Sufficient cond...

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Main Author: Bak, S.
Format: Article
Language:English
Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2018
Series:Журнал математической физики, анализа, геометрии
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/145856
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spelling irk-123456789-1458562019-02-02T01:23:10Z The Existence of Heteroclinic Travelling Waves in the Discrete Sine-Gordon Equation with Nonlinear Interaction on a 2D-Lattice Bak, S. The article deals with the discrete sine-Gordon equation that describes an infinite system of nonlinearly coupled nonlinear oscillators on a 2D-lattice with the external potential V (r) = K(1 - cos r). The main result concerns the existence of heteroclinic travelling waves solutions. Sufficient conditions for the existence of these solutions are obtained by using the critical points method and concentration-compactness principle. Статтю присвячено дискретному рiвнянню синус-Гордона, яке описує нескiнченну систему нелiнiйно зв'язаних нелiнiйних осциляторiв на двовимiрнiй гратцi iз зовнiшнiм потенцiалом V (r) = K(1 cos r). Основний результат стосується iснування розв язкiв у виглядi гетероклiнiчних рухомих хвиль. За допомогою методу критичних точок i принципу концентровано компактностi отримано достатнi умови iснування таких розв язкiв. 2018 Article The Existence of Heteroclinic Travelling Waves in the Discrete Sine-Gordon Equation with Nonlinear Interaction on a 2D-Lattice / S. Bak // Журнал математической физики, анализа, геометрии. — 2018. — Т. 14, № 1. — С. 16-26. — Бібліогр.: 19 назв. — англ. 1812-9471 DOI: https://doi.org/10.15407/mag14.01.016 Mathematics Subject Classification 2010: 34G20, 37K60, 58E50 http://dspace.nbuv.gov.ua/handle/123456789/145856 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description The article deals with the discrete sine-Gordon equation that describes an infinite system of nonlinearly coupled nonlinear oscillators on a 2D-lattice with the external potential V (r) = K(1 - cos r). The main result concerns the existence of heteroclinic travelling waves solutions. Sufficient conditions for the existence of these solutions are obtained by using the critical points method and concentration-compactness principle.
format Article
author Bak, S.
spellingShingle Bak, S.
The Existence of Heteroclinic Travelling Waves in the Discrete Sine-Gordon Equation with Nonlinear Interaction on a 2D-Lattice
Журнал математической физики, анализа, геометрии
author_facet Bak, S.
author_sort Bak, S.
title The Existence of Heteroclinic Travelling Waves in the Discrete Sine-Gordon Equation with Nonlinear Interaction on a 2D-Lattice
title_short The Existence of Heteroclinic Travelling Waves in the Discrete Sine-Gordon Equation with Nonlinear Interaction on a 2D-Lattice
title_full The Existence of Heteroclinic Travelling Waves in the Discrete Sine-Gordon Equation with Nonlinear Interaction on a 2D-Lattice
title_fullStr The Existence of Heteroclinic Travelling Waves in the Discrete Sine-Gordon Equation with Nonlinear Interaction on a 2D-Lattice
title_full_unstemmed The Existence of Heteroclinic Travelling Waves in the Discrete Sine-Gordon Equation with Nonlinear Interaction on a 2D-Lattice
title_sort existence of heteroclinic travelling waves in the discrete sine-gordon equation with nonlinear interaction on a 2d-lattice
publisher Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate 2018
url http://dspace.nbuv.gov.ua/handle/123456789/145856
citation_txt The Existence of Heteroclinic Travelling Waves in the Discrete Sine-Gordon Equation with Nonlinear Interaction on a 2D-Lattice / S. Bak // Журнал математической физики, анализа, геометрии. — 2018. — Т. 14, № 1. — С. 16-26. — Бібліогр.: 19 назв. — англ.
series Журнал математической физики, анализа, геометрии
work_keys_str_mv AT baks theexistenceofheteroclinictravellingwavesinthediscretesinegordonequationwithnonlinearinteractionona2dlattice
AT baks existenceofheteroclinictravellingwavesinthediscretesinegordonequationwithnonlinearinteractionona2dlattice
first_indexed 2023-05-20T17:23:15Z
last_indexed 2023-05-20T17:23:15Z
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