INSTABILITY MECHANISM FOR BRIGHT SOLITARY-WAVE SOLUTIONS TO THE CUBIC-QUINTIC GINZBURG-LANDAU-EQUATION

We address the stability of solitary waves to the complex cubic-quinti c Ginzburg-Landau equation near the nonlinear Schrodinger limit. It is shown that the adiabatic method does not capture all possible instabi lity mechanisms. The solitary wave can destabilize owing to discrete e igenvalues that move out of the continuous spectrum upon adding nonint egrable perturbations to the nonlinear Schrodinger equation. If an eig envalue does move out of the continuous spectrum, then we say that an edge bifurcation has occurred. We present a novel analytical technique that allows us to determine whether eigenvalues arise in such a fashi on, and if they do, to locate them. Using this approach, we show that Hopf bifurcations can arise in the cubic-quintic Ginzburg-Landau equat ion. (C) 1998 Optical Society of America [S0740-3224(98)01611-7].