Study of the two‐dimensional sine‐Gordon equation arising in Josephson junctions using meshless finite point method

In this paper, the finite point method is discussed for solving the initial‐boundary value problem associated with the sine‐Gordon equation in two‐dimensional domains arising in the Josephson junctions problem. The resulting nonlinear system is solved using an appropriate predictor‐corrector scheme....

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Bibliographic Details
Published inInternational journal of numerical modelling Vol. 30; no. 6
Main Authors Kamranian, Maryam, Dehghan, Mehdi, Tatari, Mehdi
Format Journal Article
LanguageEnglish
Published Chichester, UK John Wiley & Sons, Ltd 01.11.2017
Wiley Subscription Services, Inc
Subjects
Boundary value problems
Finite element method
finite point method
Goal programming
Josephson junction
Josephson junctions
Josephson transmission line
Meshless methods
MLS approximation
Nonlinear systems
Predictor-corrector methods
sine‐Gordon equation
Solitary waves
soliton
T junction
T shape
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ISSN0894-3370
1099-1204
DOI10.1002/jnm.2210

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Summary:In this paper, the finite point method is discussed for solving the initial‐boundary value problem associated with the sine‐Gordon equation in two‐dimensional domains arising in the Josephson junctions problem. The resulting nonlinear system is solved using an appropriate predictor‐corrector scheme. The proposed scheme is simple and efficient. The collisional properties for cases involving the most known from the bibliography, line, and ring solitons are studied in numerical results. Also the birth of a single Josephson vortex in a Josephson transmission line at a T‐shaped junction is studied.
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ISSN:0894-3370
1099-1204
DOI:10.1002/jnm.2210