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

Abstract

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.