Commun. Comput. Phys., 6 (2009), pp. 903-918.


Numerical Soliton Solutions for a Discrete Sine-Gordon System

Houde Han 1*, Jiwei Zhang 2, Hermann Brunner 3

1 Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China.
2 Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China.
3 Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, Canada A1C 5S7; and Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China.

Received 10 December 2008; Accepted (in revised version) 23 March 2009
Available online 17 April 2009

Abstract

In this paper we use an analytical-numerical approach to find, in a systematic way, new 1-soliton solutions for a discrete sine-Gordon system in one spatial dimension. Since the spatial domain is unbounded, the numerical scheme employed to generate these soliton solutions is based on the artificial boundary method. A large selection of numerical examples provides much insight into the possible shapes of these new 1-solitons.

AMS subject classifications: 65M06, 65L10, 35Q53, 35Q51

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Key words: Sine-Gordon equation, soliton solutions, numerical single solitons, artificial boundary method.

*Corresponding author.
Email: hhan@math.tsinghua.edu.cn (H. Han), jwzhang@math.hkbu.edu.hk (J. Zhang), hermann@math.mun.ca, hbrunner@math.hkbu.edu.hk (H. Brunner)
 

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