研究了带有变系数的N阶耦合非线性薛定谔方程,获得了其3-孤子解,并通过渐近分析和图像分析研究了孤子的相互作用。结果表明,当本征值不同时, 3-孤子解分别为常规孤子、束缚态孤子以及常规孤子和束缚态孤子的组合;当满足特定条件时,常规亮孤子和束缚态亮孤子可实现弹性相互作用,也可实现非弹性相互作用,而暗孤子仅存在非弹性相互作用;对于常规孤子和束缚态孤子的组合,亮孤子分量的相互作用规律较为复杂,受参数取值影响较大,但暗孤子分量依然保持弹性相互作用。

The N-order coupled nonlinear Schr dinger equation with variable coefficients is studied and its 3-soliton solutions are obtained. The soliton interaction is studied by the asymptotic analysis and graph analysis. The results show that when the eigenvalues are different, the 3-soliton solutions can be expressed as the regular solitons, the bounded solitons, and the combination of them, respectively. Under the certain conditions, both the regular bright solitons and the bounded bright solitons can realize the elastic and the inelastic interactions, respectively. However, the dark solitons only have the inelastic interaction. But for the combination of the regular and the bounded solitons, the interacting rules of the bright soliton components are very complex and significantly influenced by the value of the parameters, but the dark soliton components still maintain the elastic interaction.