title: Mobility of discrete solitons in quadratically nonlinear media.
abstract: We study the mobility of solitons in lattices with quadratic (chi(2), alias second-harmonic-generating) nonlinearity. Using the notion of the Peierls-Nabarro potential and systematic numerical simulations, we demonstrate that, in contrast with their cubic (chi(3)) counterparts, the discrete quadratic solitons are mobile not only in the one-dimensional (1D) setting, but also in two dimensions (2D), in any direction. We identify parametric regions where an initial kick applied to a soliton leads to three possible outcomes: staying put, persistent motion, or destruction. On the 2D lattice, the solitons survive the largest kick and attain the largest speed along the diagonal direction.
authors.affiliation: Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.
authors.forename: H
authors.initials: H
authors.lastname: Susanto
authors.forename: P G
authors.initials: PG
authors.lastname: Kevrekidis
authors.forename: R
authors.initials: R
authors.lastname: Carretero-González
authors.forename: B A
authors.initials: BA
authors.lastname: Malomed
authors.forename: D J
authors.initials: DJ
authors.lastname: Frantzeskakis
mesh_terms: D016880:Anisotropy; D017711:Nonlinear Dynamics