Stability of weakly nonlinear localized states in attractive potentials.
We analyze the stability of bound states to the nonlinear Schrödinger equation with an "attractive" linear potential and a cubic nonlinearity of arbitrary sign. A sufficient stability criterion is derived, which only requires knowledge of the linear modes of the potential. The results are double-checked numerically for the step-index optical fiber. An estimate of the growth rate versus nonlinearity is established in the limit of weak power.
Skupin
S
S
Institute of Condensed Matter Theory and Solid State Optics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany. stefan@pinet.uni-jena.de
Peschel
U
U
Bergé
L
L
Lederer
F
F