scholarly journals Transparent boundary conditions for the sine-Gordon equation: Modeling the reflectionless propagation of kink solitons on a line

2021 ◽  
pp. 127822
Author(s):  
K.K. Sabirov ◽  
J.R. Yusupov ◽  
M. Ehrhardt ◽  
D.U. Matrasulov
Keyword(s):  
Boundary Conditions ◽  
Gordon Equation ◽  
Equation Modeling ◽  
Sine Gordon Equation ◽  
Transparent Boundary Conditions

Split Mode Method for the Elliptic 2D Sine-Gordon Equation: Application to Josephson Junction in Overlap Geometry

1998 ◽  
Vol 09 (02) ◽  
pp. 301-323 ◽  
Author(s):  
Jean-Guy Caputo ◽  
Nikos Flytzanis ◽  
Yuri Gaididei ◽  
Irene Moulitsa ◽  
Emmanuel Vavalis
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Josephson Junction ◽  
Gordon Equation ◽  
Splitting Method ◽  
Two Dimensional ◽  
Sine Gordon Equation ◽  
Dimensional Solution ◽  
One Dimensional

We introduce a new type of splitting method for semilinear partial differential equations. The method is analyzed in detail for the case of the two-dimensional static sine-Gordon equation describing a large area Josephson junction with overlap current feed and external magnetic field. The solution is separated into an explicit term that satisfies the one-dimensional sine-Gordon equation in the y-direction with boundary conditions determined by the bias current and a residual which is expanded using modes in the y-direction, the coefficients of which satisfy ordinary differential equations in x with boundary conditions given by the magnetic field. We show by direct comparison with a two-dimensional solution that this method converges and that it is an efficient way of solving the problem. The convergence of the y expansion for the residual is compared for Fourier cosine modes and the normal modes associated to the static one-dimensional sine-Gordon equation and we find a faster convergence for the latter. Even for such large widths as w=10 two such modes are enough to give accurate results.

Split Local Artificial Boundary Conditions for the Two-Dimensional Sine-Gordon Equation on R2

2011 ◽  
Vol 10 (5) ◽  
pp. 1161-1183 ◽  
Author(s):  
Houde Han ◽  
Zhiwen Zhang
Keyword(s):  
Boundary Conditions ◽  
Gordon Equation ◽  
Splitting Method ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Computational Domain ◽  
Two Dimensional ◽  
Sine Gordon Equation ◽  
Artificial Boundary ◽  
Artificial Boundary Conditions

AbstractIn this paper the numerical solution of the two-dimensional sine-Gordon equation is studied. Split local artificial boundary conditions are obtained by the operator splitting method. Then the original problem is reduced to an initial boundary value problem on a bounded computational domain, which can be solved by the finite difference method. Several numerical examples are provided to demonstrate the effectiveness and accuracy of the proposed method, and some interesting propagation and collision behaviors of the solitary wave solutions are observed.

SOLITON TRAINS AND I–V CHARACTERISTICS OF LONG JOSEPHSON JUNCTIONS

1995 ◽  
Vol 05 (02) ◽  
pp. 491-505 ◽  
Author(s):  
A.G. MAKSIMOV ◽  
V.I. NEKORKIN ◽  
M.I. RABINOVICH
Keyword(s):  
Magnetic Field ◽  
Josephson Junction ◽  
Josephson Junctions ◽  
Gordon Equation ◽  
Alternating Magnetic Field ◽  
Equation Modeling ◽  
Sine Gordon Equation ◽  
Soliton Dynamics ◽  
Current Voltage ◽  
Current Voltage Characteristics

Soliton dynamics in a perturbed sine-Gordon equation modeling a long Josephson junction is investigated. Solitons are found to exist in both simple and chaotic forms. Soliton synchronization by an alternating magnetic field is analysed. Current-voltage characteristics of Josephson junction are plotted.

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