[1]
McLachlan, R., Symplectic integration of Hamiltonian wave equations, Numerische Mathematik, 66(1) (1993), pp. 465–492.

[2]
Feng, K. and Qin, M. Z., Symplectic difference schemes for Hamiltonian systems, in Symplectic Geometric Algorithms for Hamiltonian Systems, Springer Berlin Heidelberg, (2010), pp. 187–211.

[3]
Dahlby, M., Owren, B. and Yaguchi, T., Preserving multiple first integrals by discrete gradients, J. Phys. A Math. Theor., 44(30) (2011), 305205.

[4]
Quispel, G. R. W. and McLaren, D. I., A new class of energy-preserving numerical integration methods, J. Phys. A Math. Theor., 41(4) (2008), 045206.

[5]
Brugnano, L., Iavernaro, F. and Trigiante, D., Hamiltonian boundary value methods (energy preserving discrete line integral methods), J. Numer. Anal. Industrial Appl. Math., 5(1-2) (2010), pp. 17–37.

[6]
Brugnano, L. and Iavernaro, F., Line integral methods which preserve all invariants of conservative problems, J. Comput. Appl. Math., 236(16) (2012), pp. 3905–3919.

[7]
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.

[8]
Zhu, H. J., Tang, L. Y., Song, S. H., Tang, Y. F. and Wang, D. S., Symplectic wavelet collocation method for Hamiltonian wave equations, J. Comput. Phys., 229 (2010), pp. 2550–2572.

[9]
Qian, X., Song, S. H. and Gao, E., Explicit multi-symplectic method for the Zakharov-Kuznetsov equation, Chinese Phys. B, 21(7) (2012), pp. 43–48.

[10]
Li, H. C., Sun, J. Q. and Qin, M., Multi-symplectic method for the Zakharov-Kuznetsov equation, Adv. Appl. Math. Mech., 7(1) (2015), pp. 58–73.

[11]
Qian, X., Song, S. H. and Chen, Y. M., A semi-explicit multi-symplectic splitting scheme for a 3-coupled nonlinear Schrödinger equation, Comput. Phys. Commun., 185(4) (2014), pp. 1255–1264.

[12]
Takaharu, Y., Matsuo, T. and Sugihara, M., The discrete variational derivative method based on discrete differential forms, J. Comput. Phys., 231(10) (2012), pp. 3963–3986.

[13]
Miyatake, Y. and Matsuo, T., Conservative finite difference schemes for the Degasperis-Procesi equation, J. Comput. Appl. Math., 236(15) (2012), pp. 3728–3740.

[14]
Hairer, E., Energy-preserving variant of collocation methods, J. Numer. Anal. Industrial Appl. Math., 5 (2010), pp. 73–84.

[15]
Miyatake, Y., An energy-preserving exponentially-fitted continuous stage Runge-Kutta method for Hamiltonian systems, BIT Numer. Math., 54(3) (2014), pp. 777–799.

[16]
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., 230(20) (2012), pp. 6770–6789.

[17]
Zhang, H. and Song, S. H., Average vector field methods for the coupled Schrödinger KdV equations, Chinese Phys. B, 23(7) (2014), pp. 242–250.

[18]
Cai, J. X., Wang, Y. S. and Gong, Y. Z., Numerical analysis of AVF methods for three-dimensional time-domain Maxwell's equations, J. Sci. Comput., (2015), pp. 1–36.

[19]
Karasozen, B. and Simsek, G., Energy preserving integration of bi-Hamiltonian partial differential equations, Appl. Math. Lett., 26(12) (2013), pp. 1125–1133.

[20]
Brugnano, L., Caccia, G. F. and Iavernaro, F., Energy conservation issues in the numerical solution of the semilinear wave equation, Appl. Math. Comput., 270(C) (2015), pp. 842–870.

[21]
Brugnano, L. and Sun, Y. J., Multiple invariants conserving Runge-Kutta type methods for Hamiltonian problems, Numer. Algorithms, 65(3) (2014), pp. 611–632.

[22]
Chen, Y. M., Song, S. H. and Zhu, H. J., Explicit multi-symplectic splitting methods for the nonlinear Dirac equation, Adv. Appl. Math. Mech., 6(4) (2014), pp. 494–514.

[23]
Chen, Y. M., Song, S. H. and Zhu, H. J., Multi-symplectic methods for the Ito-type coupled KdV equation, Appl. Math. Comput., 218(9) (2012), pp. 5552–5561.

[24]
Chen, J. B. and Qin, M. Z., Multi-symplectic fourier pseudospectral method for the nonlinear Schrödinger equation, Electronic Transactions on Numerical Analysis, 12 (2001), pp. 193–204.

[25]
Ascher, U. M. and McLachlan, R. I., On symplectic and multisymplectic schemes for the KdV equation, J. Sci. Comput., 25(1) (2005), pp. 83–104.

[26]
Wei, L. L., He, Y. N. and Zhang, X. D., Analysis of an implicit fully discrete local discontinuous Galerkin method for the time-fractional Kdv equation, Adv. Appl. Math. Mech., 7(4) (2015), pp. 510–527.

[27]
Kieri, E., Kreiss, G. and Runborg, O., Coupling of Gaussian beam and finite difference solvers for semiclassical Schrödinger equations, Adv. Appl. Math. Mech., 7(6) (2015), pp. 687–714.