Strongly asymmetric soliton explosions.

We have observed, in numerical simulations, strongly asymmetric soliton explosions in dissipative systems modeled by the one-dimensional complex cubic-quintic Ginzburg-Landau equation. The explosions occur at one side of the soliton, in spite of the fact that the initial conditions and the equation itself are symmetric. From one explosion to the next, the side of the soliton where it occurs alternates, so that the left- and right-hand sides of the soliton explode successively. We give explanations for this effect based on a linear stability analysis of the unstable soliton. We also describe the transition from the stationary soliton into the exploding one as a three-stage process of soliton cooling.