Abstract High order energy preserving scheme for the strongly coupled nonlinear
Schr\"{o}dinger system is proposed by the average vector field method.
The high order energy preserving scheme is applied to simulate solitons
evolution of the strongly coupled Schr\"{o}dinger system. Numerical results show that
the high order energy preserving scheme can well simulate solitons
evolution, moreover preserve the discrete energy of the
strongly coupled nonlinear Schr\"{o}dinger system exactly.
