Nonlinear localized waves in a periodic medium
arXiv:nlin/0010055 · doi:10.1103/PhysRevLett.87.083901
Abstract
We analyze the existence and stability of nonlinear localized waves in a periodic medium described by the Kronig-Penney model with a nonlinear defect. We demonstrate the existence of a novel type of stable nonlinear band-gap localized states, and also reveal an important physical mechanism of the oscillatory wave instabilities associated with the band-gap resonances.
4 pages, 5 figures
References in corpus (7)
- Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates
- Bose-Einstein condensates in standing waves: The cubic nonlinear Schroedinger equation with a periodic potential
- Creation of gap solitons in Bose-Einstein condensates
- Parametric localized modes in quadratic nonlinear photonic structures
- Bose-Einstein Condensates in Optical Lattices: Spontaneous Emission in the Presence of Photonic Band Gaps
- Spontaneous emission of polaritons from a Bose-Einstein condensate
- Electron locking in semiconductor superlattices
Cited by in corpus (22)
- Solitons in nonlinear lattices
- Bose-Einstein Condensates in Optical Lattices: Band-Gap Structure and Solitons
- Bifurcations and stability of gap solitons in periodic potentials
- Defect modes in one-dimensional photonic lattices
- Stopping Light on a Defect
- Spatial optical solitons in nonlinear photonic crystals
- Multi-gap discrete vector solitons
- Generation and stability of discrete gap solitons
- Nonlinear Band Structure in Bose Einstein Condensates: The Nonlinear Schrödinger Equation with a Kronig-Penney Potential
- Two-dimensional defect modes in optically induced photonic lattices
- Period doubling, two-color lattices, and the growth of swallowtails in Bose-Einstein condensates
- Nonlinear localized modes at phase-slip defects in waveguide arrays
- Interlaced linear-nonlinear optical waveguide arrays
- Instabilities and Bifurcations of Nonlinear Impurity Modes
- Quasi-compactons in inverted nonlinear photonic crystals
- Perturbation-induced radiation by the Ablowitz-Ladik soliton
- Observation of localized modes at phase slips in two-dimensional photonic lattices
- Amplitude squeezed fiber Bragg grating solitons
- Two-dimensional intra-band solitons in lattice potentials with local defects and self-focusing nonlinearity
- Solitons supported by singular modulation of the cubic nonlinearity
- Nondecaying linear and nonlinear modes in a periodic array of spatially localized dissipations
- Soliton shape and mobility control in optical lattices