[1]
Bibi, N., Tirmizi, S. I. A. and Haq, S., Meshless method of lines numerical solution of Kawahara-Type equations, Appl. Math., 2 (2011), pp. 608–618.

[2]
Bridges, T. J., Multi-symplectic structures and wave propagation, Math. Proc. Cambridge Philos. Soc., 121 (1997), pp. 147–190.

[3]
Bridges, T. J. and Reich, S., Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity, Phys. Lett. A, 284 (2001), pp. 184–193.

[4]
Cai, J. X. and Wang, Y. S., A conservative Fourier pseudospectral algorithm for a coupled nonlinear Schrödinger system, China Phys. B, 22 (2013), 060207.

[5]
Cai, J. X. and Wang, Y. S., Local structure-preserving algorithms for the “good” Boussinesq equation, J. Comput. Phys., 239 (2013), pp. 72–89.

[6]
Cai, J. X., Wang, Y. S. and Liang, H., Local energy-preserving and momentum-preserving algorithms for coupled nonlinear Schröinger system, J. Comput. Phys., 239 (2013), pp. 30–50.

[7]
Ceballos, J. C., Sepúlveda, M. and Villagrán, O. P. V., The KdV-Kawahara equation in a bounded domain and some numerical results, Appl. Math. Comput., 190 (2007), pp. 912–936.

[8]
Celledoni, E., Grimm, V., McLachlan, R. I., McLaren, D. I., O'Neale, D., Owren, B. and Quispel, G. R. W., Preserving energy resp. dissipation in numerical PDEs using the “Average Vector Field” method, J. Comput. Phys., 231 (2012), pp. 6770–6789.

[9]
Celledoni, E., McLachlan, R. I., McLaren, D. I., Owren, B., Quispel, G. R. W. and Wright, W. M., Energy-preserving Runge-Kutta methods, ESAIM: Math. Model. Numer. Anal., 43 (2009), pp. 645–649.

[10]
Chen, Y., Sun, Y. J. and Tang, Y. F., Energy-preserving numerical methods for Landau-Lifshitz equation, J. Phys. A Math. Theor., 44 (2011), 295207.

[11]
Chen, Y. M., Zhu, H. J. and Song, S. H., Multi-symplectic splitting method for the coupled nonlinear Schrödinger equation, Comput. Phys. Commun., 181 (2010), pp. 1231–1241.

[12]
Cui, Y. F. and Mao, D. K., Numerical method satisfying the first two conservation laws for the Korteweg-de Vries equation, J. Comput. Phys., 227 (2007), pp. 376–399.

[13]
Fei, Z. and Vázquez, L., Two energy conserving numerical schemes for the Sine-Gordon equation, Appl. Math. Comput., 45 (1991), pp. 17–30.

[14]
Feng, K. and Qin, M. Z., The Symplectic Methods for Computation of Hamiltonian Systems, Berlin: Springer, (1987), pp. 1–37.

[15]
Feng, K. and Qin, M. Z., Symplectic Geometric Algorithms for Hamiltonian Systems, Berlin/Hangzhou: Springer-Verlag/Zhejiang Publishing United Group, Zhejiang Science and Technology Publishing House, 2003.

[16]
Fla, T., A numerical energy conserving method for the DNLS equation, J. Comput. Phys., 101 (1992), pp. 71–79.

[17]
Furihata, D., Finite difference schemes for that inherit energy conservation or dissipation property, J. Comput. Phys., 156 (1999), pp. 181–205.
[18]
Gong, Y. Z., Cai, J. X. and Wang, Y. S., Some new structure-preserving algorithms for general multi-symplectic formulations of Hamiltonian PDEs, J. Comput. Phys., 279 (2014), pp. 80–102.

[19]
Hairer, E., Energy-preserving variant of collocation methods, J. Numer. Anal. Ind. Appl. Math., 5 (2010), pp. 73–84.

[20]
Hairer, E., Lubich, C. and Wanner, G., Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Diffenential Equations, Berlin: Springer-Verlag, 2006.

[21]
Hu, W. P. and Deng, Z. C., Multi-symplectic method for generalized fifth-order KdV equation, China Phys. B, 17 (2008), 3923.

[22]
Kaya, D. and Al-Khaled, K., A numerical comparision of a Kawahara equation, Phys. Lett. A, 363 (2007), pp. 433–439.

[23]
Marsden, J., Patrick, G. and Shkoller, S., Mulltisymplectic geometry, variational integrators and nonlinear PDEs, Commun. Math. Phys., 199 (1998), pp. 351–395.

[24]
Matsuo, T. and Furihata, D., Dissipative or conservative finite-difference schemes for complex-valued nonlinear partial differential equations, J. Comput. Phys., 171 (2001), pp. 425–447.

[25]
McLachlan, R. I., Quispel, G. R. W. and Robidoux, N., Geometric integration using discrete gradients, Philos. Trans. R. Soc. A, 357 (1999), pp. 1021–1046.

[26]
Quispel, G. R. W. and McLaren, D. I., A new class of energy-preserving numerical integration methods, J. Phys. A Math. Theor., 41 (2008), 045206.

[27]
Shen, J. and Tang, T., Spectral and High-order Methods with Applications, Science Press, 2006.

[28]
Wang, Y. S., Wang, B. and Qin, M. Z., Local structure-preserving algorithms for partial differential equations, Sci. China Ser. A, 51 (2008), pp. 2115–2136.

[29]
Yuan, J. M., Shen, J. and Wu, J. H., A Dual-Petrov-Galerkin method for the Kawahara-Type equation, J. Sci. Comput., 34 (2008), pp. 48–63.