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

Abstract

The stability of the bright solitary wave solution to the perturbed cubic-quintic Schroedinger 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 eigenvalue. Furthermore, it is shown that in the complimentary region of parameter space there 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.

28 pages, LaTeX, submitted; author info at http://www.math.unm.edu/~kapitula

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