Effect of an external periodic potential on pairs of dissipative solitons

We study dissipative soliton pair solutions of the complex cubic-quintic Ginzburg-Landau equation with periodic phase modulation term. The external modulation changes the soliton-pair time separation as well as their phase difference, without destroying the existing two-soliton bound state. Transitions between different stable forms of the pair occur in the form of bifurcations. Quite remarkably, two types of bound states may coexist, which leads to hysteresis loops when the modulation depth is varied