Instabilities and splitting of pulses in coupled Ginzburg-Landau equations

We introduce a general system of two coupled cubic complex Ginzburg-Landau (GL) equations that admits exact solitary-pulse (SP) solutions with a stabl e zero background. Besides representing a class of systems of the GL type, it also describes a dual-core nonlinear optical fiber with gain in one core and losses in the other. By means of systematic simulations, we study gene ric transformations of SPs in this system, which turn out to be: cascading multiplication of pulses through a subcritical Hopf bifurcation, which even tually leads to a spatio-temporal chaos; splitting of SP into stable travel ing pulses; and a symmetry-breaking bifurcation transforming a standing SP into a traveling one. In some parameter region, the Hopf bifurcation is fou nd to be supercritical, which gives rise to stable breathers. Travelling br eathers are also possible in the system considered. In a certain parameter region, stable standing SPs, moving permanent-shape ones, and traveling bre athers all coexist. In that case, we study collisions between various types of the pulses, which, generally, prove to be strongly inelastic. (C) 2001 Elsevier Science B.V. All rights reserved.