1 Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Plasma Physics and Technology Programme, Risø National Laboratory for Sustainable Energy, Technical University of Denmark3 Risø National Laboratory for Sustainable Energy, Technical University of Denmark4 Australian National University5 Department of Photonics Engineering, Technical University of Denmark6 Department of Physics, Technical University of Denmark7 Department of Applied Mathematics and Computer Science, Technical University of Denmark8 Australian National University
We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types of nonlinear impurity modes, one- and two-hump symmetric localized modes and asymmetric localized modes, for both focusing and defocusing nonlinearity and two different (attractive or repulsive) types of impurity. We obtain an analytical stability criterion for the nonlinear localized modes and consider the case of a power-law nonlinearity in detail. We discuss several scenarios of the instability-induced dynamics of the nonlinear impurity modes, including the mode decay or switching to a new stable state, and collapse at the impurity site.
Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 2001, Vol 63, Issue 3