title: Localization and delocalization of two-dimensional discrete solitons pinned to linear and nonlinear defects.
abstract: We study the dynamics of two-dimensional (2D) localized modes in the nonlinear lattice described by the discrete nonlinear Schrödinger equation, including a local linear or nonlinear defect. Discrete solitons pinned to the defects are investigated by means of the numerical continuation from the anticontinuum limit and also using the variational approximation, which features a good agreement for strongly localized modes. The models with the time-modulated strengths of the linear or nonlinear defect are considered too. In that case, one can temporarily shift the critical norm, below which localized 2D modes cannot exist, to a level above the norm of the given soliton, which triggers the irreversible delocalization transition.
authors.affiliation: Centro de Física do Porto, Faculdade de Ciências, Universidade do Porto, R. Campo Alegre 687, P-4169-007 Porto, Portugal. brazhnyy@gmail.com
authors.forename: Valeriy A
authors.initials: VA
authors.lastname: Brazhnyi
authors.forename: Boris A
authors.initials: BA
authors.lastname: Malomed