Sine-Gordon solitons in networks: Scattering and transmission at vertices

被引：29

作者：

Sobirov, Zarif ^{[1
,3
]}

Babajanov, Doniyor ^{[2
]}

Matrasulov, Davron ^{[2
]}

Nakamura, Katsuhiro ^{[4
,5
]}

Uecker, Hannes ^{[6
]}

机构：

[1] Tashkent Financial Inst, 60A Amir Temur Str, Tashkent 100000, Uzbekistan

[2] Turin Polytech Univ, 17 Niyazov Str, Tashkent 100095, Uzbekistan

[3] Natl Univ Uzbekistan Vuzgorodok, Fac Math, Tashkent 100174, Uzbekistan

[4] Natl Univ Uzbekistan Vuzgorodok, Fac Phys, Tashkent 100174, Uzbekistan

[5] Osaka City Univ, Dept Appl Phys, Osaka 5588585, Japan

[6] Carl von Ossietzky Univ Oldenburg, Inst Math, D-26111 Oldenburg, Germany

来源：

EPL | 2016年 / 115卷 / 05期

关键词：

CONSERVATION-LAWS; JUNCTION;

D O I：

10.1209/0295-5075/115/50002

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider the sine-Gordon equation on metric graphs with simple topologies and derive vertex boundary conditions from the fundamental conservation laws together with successive space-derivatives of sine-Gordon equation. We analytically obtain traveling-wave solutions in the form of standard sine-Gordon solitons such as kinks and antikinks for star and tree graphs. We show that for this case the sine-Gordon equation becomes completely integrable just as in case of a simple 1D chain. This simple analysis provides a cornerstone for the numerical solution of the general case, including a quantification of the vertex scattering. Applications of the obtained results to Josephson junction networks and DNA double helix are discussed. Copyright (C) EPLA, 2016

引用

页数：6

共 32 条

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Ablowitz M.J., 1991, Nonlinear Evolution Equations and Inverse Scattering

[2]

ABLOWITZ M. J, 2006, SOLITONS INVERSE SCA

[3] Stationary states of NLS on star graphs [J].