Instabilities and Bifurcations of Nonlinear Impurity Modes
arXiv:nlin/0302010 · doi:10.1103/PhysRevE.67.046604
Abstract
We study the structure and stability of nonlinear impurity modes in the discrete nonlinear Schr{ö}dinger equation with a single on-site nonlinear impurity emphasizing the effects of interplay between discreteness, nonlinearity and disorder. We show how the interaction of a nonlinear localized mode (a discrete soliton or discrete breather) with a repulsive impurity generates a family of stationary states near the impurity site, as well as examine both theoretical and numerical criteria for the transition between different localized states via a cascade of bifurcations.
8 pages, 8 figures, Phys. Rev. E in press
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- Anderson localization of solitons in optical lattices with random frequency modulation
- Breather Statics and Dynamics in Klein--Gordon Chains with a Bend
- Soliton percolation in random optical lattices
- Discrete peakons
- Eigenstates and instabilities of chains with embedded defects
- Complete Delocalization in a Defective Periodic Structure
- Soliton shape and mobility control in optical lattices
- Breathers in inhomogeneous nonlinear lattices: an analysis via centre manifold reduction