The stationary sine-Gordon equation on metric graphs: Exact analytical solutions for simple topologies

K. Sabirov; S. Rakhmanov; D. Matrasulov; H. Susanto

doi:10.1016/j.physleta.2017.12.057

The stationary sine-Gordon equation on metric graphs: Exact analytical solutions for simple topologies

K. Sabirov
, S. Rakhmanov
, D. Matrasulov
, H. Susanto

Mathematics

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

20 Scopus citations

Abstract

We consider the stationary sine-Gordon equation on metric graphs with simple topologies. Exact analytical solutions are obtained for different vertex boundary conditions. It is shown that the method can be extended for tree and other simple graph topologies. Applications of the obtained results to branched planar Josephson junctions and Josephson junctions with tricrystal boundaries are discussed.

Original language	British English
Pages (from-to)	1092-1099
Number of pages	8
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	382
Issue number	16
DOIs	https://doi.org/10.1016/j.physleta.2017.12.057
State	Published - 26 Apr 2018

Keywords

Jacobi's elliptic functions
Metric graphs
The Gibbs free-energy functional
The star graph
The stationary sine-Gordon equation

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10.1016/j.physleta.2017.12.057

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title = "The stationary sine-Gordon equation on metric graphs: Exact analytical solutions for simple topologies",

abstract = "We consider the stationary sine-Gordon equation on metric graphs with simple topologies. Exact analytical solutions are obtained for different vertex boundary conditions. It is shown that the method can be extended for tree and other simple graph topologies. Applications of the obtained results to branched planar Josephson junctions and Josephson junctions with tricrystal boundaries are discussed.",

keywords = "Jacobi's elliptic functions, Metric graphs, The Gibbs free-energy functional, The star graph, The stationary sine-Gordon equation",

author = "K. Sabirov and S. Rakhmanov and D. Matrasulov and H. Susanto",

note = "Funding Information: We thank Dmitry Pelinovsky for his useful comments on the paper. This work is supported by a grant of the Volkswagen Foundation and by grants of the Agency for Science and Technology of Uzbekistan (Refs. No. F-2-003 and BF-2-022 ). HS would like to acknowledge The Physical Society of Uzbekistan for the invitation and partial financial support to attend a workshop in Tashkent organized by the society. Funding Information: We thank Dmitry Pelinovsky for his useful comments on the paper. This work is supported by a grant of the Volkswagen Foundation and by grants of the Agency for Science and Technology of Uzbekistan (Refs. No. F-2-003 and BF-2-022). HS would like to acknowledge The Physical Society of Uzbekistan for the invitation and partial financial support to attend a workshop in Tashkent organized by the society. Publisher Copyright: {\textcopyright} 2018 Elsevier B.V.",

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AU - Sabirov, K.

AU - Rakhmanov, S.

AU - Matrasulov, D.

AU - Susanto, H.

N1 - Funding Information: We thank Dmitry Pelinovsky for his useful comments on the paper. This work is supported by a grant of the Volkswagen Foundation and by grants of the Agency for Science and Technology of Uzbekistan (Refs. No. F-2-003 and BF-2-022 ). HS would like to acknowledge The Physical Society of Uzbekistan for the invitation and partial financial support to attend a workshop in Tashkent organized by the society. Funding Information: We thank Dmitry Pelinovsky for his useful comments on the paper. This work is supported by a grant of the Volkswagen Foundation and by grants of the Agency for Science and Technology of Uzbekistan (Refs. No. F-2-003 and BF-2-022). HS would like to acknowledge The Physical Society of Uzbekistan for the invitation and partial financial support to attend a workshop in Tashkent organized by the society. Publisher Copyright: © 2018 Elsevier B.V.

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N2 - We consider the stationary sine-Gordon equation on metric graphs with simple topologies. Exact analytical solutions are obtained for different vertex boundary conditions. It is shown that the method can be extended for tree and other simple graph topologies. Applications of the obtained results to branched planar Josephson junctions and Josephson junctions with tricrystal boundaries are discussed.

AB - We consider the stationary sine-Gordon equation on metric graphs with simple topologies. Exact analytical solutions are obtained for different vertex boundary conditions. It is shown that the method can be extended for tree and other simple graph topologies. Applications of the obtained results to branched planar Josephson junctions and Josephson junctions with tricrystal boundaries are discussed.

KW - Jacobi's elliptic functions

KW - Metric graphs

KW - The Gibbs free-energy functional

KW - The star graph

KW - The stationary sine-Gordon equation

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JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 16

ER -

The stationary sine-Gordon equation on metric graphs: Exact analytical solutions for simple topologies

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Keywords

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