Sukhorukov AA, Kivshar YS, Bang O, Rasmussen JJ, Christiansen PL. Nonlinearity and disorder: classification and stability of nonlinear impurity modes.
Phys Rev E Stat Nonlin Soft Matter Phys 2001;
63:036601. [PMID:
11308782 DOI:
10.1103/physreve.63.036601]
[Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2000] [Indexed: 05/23/2023]
Abstract
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.
Collapse