Commun. Comput. Phys., 10 (2011), pp. 1161-1183.


Split Local Artificial Boundary Conditions for the Two-Dimensional Sine-Gordon Equation on R^2

Houde Han 1*, Zhiwen Zhang 1

1 Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China.

Received 5 June 2010; Accepted (in revised version) 2 December 2010
Available online 2 August 2011
doi:10.4208/cicp.050610.021210a

Abstract

In 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.

AMS subject classifications: 52B10, 65D18, 68U05, 68U07

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Key words: Sine-Gordon equation, operator splitting method, artificial boundary condition, soliton, unbounded domain.

*Corresponding author.
Email: hhan@math.tsinghua.edu.cn (H. Han), zhangzhiwen02@mails.tsinghua.edu.cn (Z. Zhang)
 

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