Keywords: 
• 二维饱和非线性薛定谔方程 /
• 辛几何算法 /
• 空间孤立子 /
• 冷原子EIT介质

Abstract: Optical solitons in gaseous atomic media display many striking features under electromagnetically induced transparency（EIT）. Study of theoretical model,which describes these features of optical solitons,has important meaning in optical informational process and propagation.Two-dimensional saturated nonlinear Schrodinger equation,which describes the spatial soliton evolution in the threelevel gaseous atomic EIT media,is transformed into the Hamilton system with the symplectic structure.The Hamilton system is discretizated by the symplectic method.The corresponding symplectic scheme is obtained.Evolution behaviors of two and four spatial solitons with the same amplitude in a three-level,gaseous atomic EIT media are simulated by the symplectic scheme.Numerical results further show that the phase difference and the direction of the entering gauss beams have an obvious effect on the interaction of multi-solitons.The entering Gauss beam can form the stable optical solitons in a gaseous atomic media.