[1] P. J. Caudrey, I. C. Eilbeck and J. D. Gibbon, “The Sine-Gordon Equation as a Model Classical Field Theory,” Nuovo Cimento, Vol. 25, No. 2, 1975, pp. 497-511.
[2] R. K. Dodd, I. C. Eilbeck, J. D. Gibbon and H. C. Morris, “Solitons and Nonlinear Wave Equations,” Academic, London, 1982.
[3] Sirendaoreji, “Auxiliary Equation Method and New Solutions of Klein-Gordon Equations,” Chaos, Solitons & Fractals, Vol. 31, No. 4, 2007, pp. 943-950. doi:10.1016/j.chaos.2005.10.048
[4] Sirendaoreji, “A New Auxiliary Equation and Exact Travelling Wave Solutions of Nonlinear Equation,” Physics Letters A, Vol. 356, No. 2, 2006, pp. 124-130. doi:10.1016/j.physleta.2006.03.034
[5] A. M. Wazwaz, “New Travelling Wave Solutions to the Boussinesq and Klein-Gordon Equations,” Communications in Nonlinear Science and Numerical Simulation, Vol. 13, No. 5, 2008, pp. 889-901. doi:10.1016/j.cnsns.2006.08.005
[6] M. A. Lynch, “Large Amplitude Instability in Finite Difference Approximates to the Klein-Gordon Equation,” Applied Numerical Mathematics, Vol. 31, No. 2, 1999, pp. 173-182. doi:10.1016/S0168-9274(98)00128-7
[7] X. Li, B. Y. Guo and L. Vazquez, “A Legendre Spectral Method for Solving the Nonlinear Klein-Gordon Equation,” Mathematics Applied and Computation, Vol. 15, No. 1, 1996, pp. 19-36.
[8] X. Li and B. Y. Guo, “A Legendre Spectral Method for Solving Nonlinear Klein-Gordon Equation,” Journal Computation of Mathematics, Vol. 15, No. 2, 1997, pp. 105-126.
[9] M. Deghan and A. Shokri, “Numerical Solution of the Nonlinear Klein-Gordon Equation Using Radial Basis Functions,” Journal of Computational and Applied Mathematics, Vol. 230, No. 2, 2009, pp. 400-410. doi:10.1016/j.cam.2008.12.011
[10] R. Benzi, S. Succi and M. Vergassola, “The Lattice Boltzmann Equation: Theory and Application,” Physics Reports, Vol. 222, No. 3, 1992, pp. 145-197. doi:10.1016/0370-1573(92)90090-M
[11] S. Y. Chen and G. D. Doolen, “Lattice Boltzmann Method for Fluid Flows,” Annual Review of Fluid Mechanics, Vol. 30, No. 1, 1997, pp. 329-364. doi:10.1146/annurev.fluid.30.1.329
[12] J. Y. Zhang, G. W. Yan and Y. F. Dong, “A New Lattice Boltzmann Model for the Laplace Equation,” Applied Mathematics and Computation, Vol. 215, No. 2, 2009, pp. 539-547.doi:10.1016/j.amc.2009.05.047
[13] Z. H. Chai and B. C. Shi, “A Novel Lattice Boltzmann Model for the Poisson Equation,” Applied Mathematical Modelling, Vol. 32, No. 10, 2008, pp. 2050-2058. doi:10.1016/j.apm.2007.06.033
[14] M. Hirabayashi, Y. Chen and H. Ohashi, “The Lattice BGK Model for the Poisson Equation,” JSME International Journal Series B, Vol. 44, No. 1, 2001, pp. 45-52. doi:10.1299/jsmeb.44.45
[15] J. G. Zhou, “Lattice Boltzmann Method for Shallow Water Flows,” Springer Verlag, New York, 2004.
[16] Z. Shen, G. Yuan and L. Shen, “Lattice Boltzmann Method for Burgers Equation,” Chinese Journal of Computational Physics, Vol. 175, No. 1, 2000, pp. 172-177.
[17] J. Y. Zhang and G. W. Yan, “A Lattice Boltzmann Model for the Korteweg-de Vries Equation with Two Conservation Laws,” Computer Physics Communications, Vol. 180, No. 7, 2009, pp. 1054-1062. doi:10.1016/j.cpc.2008.12.027
[18] G. W. Yan, “A Lattice Boltzmann Equation for Waves,” Journal of Computational Physics, Vol. 161, No. 1, 2000, pp. 61-69. doi:10.1006/jcph.2000.6486
[19] J. Y. Zhang, G. W. Yan and X. Shi, “Lattice Boltzmann Model for Wave Propagation,” Physics Review E, Vol. 80, 2009, Article ID 026706. doi:10.1103/PhysRevE.80.026706
[20] S. P. Dawson, S. Chen and G. D. Doolen, “Lattice Boltzmann Computations for Reaction-Diffusion Equation,” Journal of Chemical Physics, Vol. 98, No. 2, 1993, pp. 1514-1523. doi:10.1063/1.464316
[21] X. Yu and B. C. Shi, “A Lattice Boltzmann Model for Reaction Dynamical Systems with Time Delay,” Applied Mathematics and Computation, Vol. 181, No. 2, 2006, pp. 958-965. doi:10.1016/j.amc.2006.02.020
[22] S. R. Vander and M. Ernst, “Convection-Diffusion Lattice Boltzmann Scheme for Irregular Lattice,” Journal of Computational Physics, Vol. 160, No. 2, 2000, pp. 766-782. doi:10.1006/jcph.2000.6491
[23] Z. L. Guo, B. C. Shi and N. C. Wang, “Fully Lagrangian and Lattice Boltzmann Method for the Advection-Diffusion Equation,” Journal of Scientific Computing, Vol. 14, No. 3, 1999, pp. 291-300. doi:10.1023/A:1023273603637
[24] B.C. Shi and Z. L. Guo, “Lattice Boltzmann Model for Nonlinear Convection-Diffusion Equations,” Physics Review E, Vol. 79, 2009, Article ID 016701. doi:10.1103/PhysRevE.79.016701
[25] Z. L. Guo, C. G. Zheng and B. C. Shi, “Non-Equilibrium Extrapolation Method for Velocity and Pressure Boundary Conditions in the Lattice Boltzmann Method,” Chinese Physics, Vo. 11, No. 4, 2002, pp. 366-374. doi:10.1088/1009-1963/11/4/310
[26] S. Jiminez and L. Vazquez, “Analysis of Four Numerical Scheme for a Nonlinear Klein-Gordon Equation,” Applied Mathematics and Computation, Vol. 35, No. 1, 1990, pp. 61-94. doi:10.1016/0096-3003(90)90091-G