Simultaneous existence of a multiplicity of stable and unstable solitons in dissipative systems

We show that dissipative systems can have a multiplicity of stationary solutions in the form of both stable and unstable solitons. As a model equation, we use the complex cubic-quintic Ginzburg-Landau equation. For a given set of the equation parameters, this equation has many coexisting soliton solutions. Our stability results show that although most of them are unstable, they can have stable pieces. This partial stability leads to the phenomenon of soliton explosion. (C) 2001 Elsevier Science B.V All rights reserved.