对非线性光纤中（3+1）维耦合非线性薛定谔系统中明孤子和暗孤子的解析研究

Under investigation in this paper is a $(3+1)$-dimensional coupled nonlinear Schr"{o}dinger system, which describes the dynamics of solitons formed by the pulse envelopes respectively along the orthogonal fast and slow birefringence axes in the bulk Kerr and saturable media in nonlinear optical fibres. Via the symbolic computation and Hirota method, analytic bright one- and dark one-soliton solutions for such a system are obtained. Graphic description of the soliton properties is illustrated. Through the analysis on bright and dark one-soliton properties, it can be found that the bright soliton amplitude and dark soliton width depend on the index of refraction: when the value of the index of refraction increases, bright soliton amplitude become larger and dark soliton width become larger.