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Boundary problem with double sine-Gordon equation and Neuman conditions: analysis of the physical parameters influence on the analytical solutions applicability and phase portraits

Atanasova P.Kh., Panayotova S.A.1

Joint institute for nuclear research, 6 Joliot-Curie St, Dubna, 141980, Dubna, poli@jinr.ru

1University of Plovdiv “Paisii Hilendarski”, 24 Tzar Asen, Plovdiv, 4000, Bulgaria, stefani.panaiotova93@gmail.com

The aim of our work is to obtain all types of analytical solutions of the boundary problem with double sine-Gordon equation and Neuman conditions. This task is very relevant in the study of long Josephson contacts with a second harmonic in the current-phase distribution. Work in this area has started relatively recently and the results obtained so far are presented in the articles [1,2]. The main issue raised was the applicability of the analytical expressions obtained. In this work classification and comprehensive analysis of the physical parameters under which it is possible to implement each of the solutions is made. Influence of the problem parameters on the change of the phase portraits is analyzed.

1. H.D.Dimov , P.Kh.Atanasova and S.A.Panayotova, Some analitical solutions for magnetic flux distribution in long josephson junction with second harmonic in the current phase relation, AIP Conference Proceedings 2164, 100001 (2019)

2. Pavlina Khristova Atanasova, Hristo Dimov Dimov, Analitical solutions of a double sine-Gordon stationary equation describing long Josephson junctions , Proceedings of the Scientific Conference Innovative ICT in Research and Education: Mathematics, Informatics and Information Technologies, Pamporovo, 29-30 November 2018, Section A: Development of Innovative Software Tools and Technologies with Application in Research and Business, 2019, стр.105-116, 2019

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