2000/09/03 by Andrey A. Sukhorukov, Yuri S. Kivshar, Ole Bang +4
Mathematics · Physics and Astronomy · #Advanced Fiber Laser Technologies #Advanced Mathematical Physics Problems #Computer science #Condensed matter physics #Impurity #Instability #Mode (computer interface) #Nonlinear Photonic Systems #Nonlinear system #Physics #Quantum mechanics #Stability (learning theory) #Statistical physics #nlin.PS
paper · pdf · doi:10.1103/physreve.63.036601
published as Phys. Rev. E 63, 036601(1-18) (2001) · 18 pages, 22 figures
arxiv created 2000/09/03 · openalex publication_date 2001/02/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.