Stability criterion for bright solitary waves of the perturbed cubic-quintic Schrodinger equation

The stability of the bright solitary wave solution to the perturbed cubic-quintic Schrodinger equation is considered. It is shown that in a certain region of parameter space these solutions are unstable, with the instability being manifested as a small positive eignevalue. Furthermore, it is shown that in the complimentary region of parameter space then are no small unstable eigenvalues. The proof involves a novel calculation of the Evans function: which is of interest in its own right. As a consequence of the eigenvalue calculation, it is additionally shown that N-bump bright solitary waves bifurcate from the primary wave. Copyright (C) 1998 Elsevier Science B.V.