Abstract: The fifth order saturated nonlinear Schrödinger equation is transformed into the multi-symplecticstructure and discretizated by the middle Preissman scheme.The multi-symplectic scheme and the corresponding multi-symplectic conservation is obtained.The solitary waves with different nonlinear saturated effects and different amplitude are simulated by the multi-symplectic scheme.Numerical results show the multi-symplectic scheme can well simulate the behaviors of optical solitons and approximately preserve the energy conservation property.Nonlinear saturated effects and the amplitude have obvious effect on the propagation of the solitary waves and the collision of the solitary waves also have obvious effect on the change of the system energy.

Key words: fifth order saturated nonlinear Schrö, dinger equation, multi-symplectic method, solitary wave