1997/01/23 by Todd Kapitula · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #nlin.PS #patt-sol
paper · pdf · doi:10.1016/s0167-2789(97)00245-5
28 pages, LaTeX, submitted; author info at http://www.math.unm.edu/~kapitula
arxiv created 1997/01/23 · arxiv updated 2009/11/30
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.