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Numerical Study of the Nonlinear Combined Sine-Cosine-Gordon Equation with the Lattice Boltzmann Method

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Abstract

In this paper, a lattice Boltzmann model is developed for solving the combined sine-cosine-Gordon equation through selecting equilibrium distribution function properly. With the Chapman-Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. Some problems, which have exact solutions, are validated by the present model. From the simulations, we find that the numerical results agree well with the exact solutions or better than the numerical solutions reported in previous studies. The study indicates that the present method is very effective and accurate. The present model can be used to solve more other nonlinear wave problems.

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Acknowledgements

The authors sincerely thank the anonymous reviewers for their valuable comments and suggestions, which are very helpful for revising the paper. Also, One of the authors (Huilin Lai) warmly thanks Dr. Qing Li (University of Southampton), Dr. Jie Liao (East China University of Science and Technology), and Dr. Yanbiao Gan (Institute of Applied Physics and Computational Mathematics) for their helpful discussions, suggestions, and encouragements during this work.

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  1. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, 350007, China

    Huilin Lai & Changfeng Ma

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  1. Huilin Lai
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  2. Changfeng Ma
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Correspondence to Changfeng Ma.

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The project is supported by National Natural Science Foundation of China (Grant No. 10831005, 11071041).

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Lai, H., Ma, C. Numerical Study of the Nonlinear Combined Sine-Cosine-Gordon Equation with the Lattice Boltzmann Method. J Sci Comput 53, 569–585 (2012). https://doi.org/10.1007/s10915-012-9587-6

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