有耗孤子的最小作用量原理及其在二维光子带隙结构中的应用

采用变分方法对于二维矩形光子带隙结构中X点孤子的耗散以及相干作用进行了动力学分析.通过对由作用量原理得到的孤子参量联立方程组的分析可知，除了耗散作用导致孤子的幅度衰减，并引起孤子横向的展宽以外，同向孤子的相互作用负势函数为耗散作用所减弱，从而使得孤子在x方向的束缚态被削弱.孤子中心间距随x的增加呈现出增幅变化且波动周期增大，当纵向距离增大到一定值后，孤子中心间距将一直增大下去.

Least action principle for dissipative solitons and its application in two-dimensional PBG structure

Dissipative and coherent effects of X-point solitons are investigated on the basis of dynamic variational formulation in two-dimensional photonic bandgap (PBG) structure of square lattice. Through the least action principle, the result deduced from analyzing soliton parametric equations indicates that dissipative effect leads to not only amplitude decrease but also section expansion of solitons. In addition, co-soliton interaction for negative potential is decreased by dissipation, and bound sate of solitons in x direction is also weakened. Amplitude and period of fluctuation of relative interval between soliton centers increase in x direction, when x increases to some value, relative interval will increase continuously.