Volume 115, Number 5, September 2016
|Number of page(s)||6|
|Published online||05 October 2016|
Sine-Gordon solitons in networks: Scattering and transmission at vertices
1 Tashkent Financial Institute - 60A, Amir Temur Str., Tashkent 100000, Uzbekistan
2 Turin Polytechnic University in Tashkent - 17 Niyazov Str., Tashkent 100095, Uzbekistan
3 Faculty of Mathematics, National University of Uzbekistan - Vuzgorodok, Tashkent 100174, Uzbekistan
4 Faculty of Physics, National University of Uzbekistan - Vuzgorodok, Tashkent 100174, Uzbekistan
5 Department of Applied Physics, Osaka City University - Osaka 558-8585, Japan
6 Institut für Mathematik, Universität Oldenburg - D-26111 Oldenburg, Germany
Received: 9 April 2016
Accepted: 8 September 2016
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.
PACS: 05.45.Yv – Solitons / 02.30.Ik – Integrable systems / 42.65.Tg – Optical solitons; nonlinear guided waves
© EPLA, 2016
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