title: One- and two-dimensional solitons in second-harmonic-generating lattices.
abstract: In a model of a dynamical lattice with the on-site second-harmonic-generating nonlinearity and harmonic intersite couplings (that may be equal or different for the fundamental and second harmonics), various solitary-wave solutions are considered in one and two dimensions (1D and 2D). Fundamental (single-hump) solitons are identified in either dimension and their stability is examined and compared to previous results as well as to what is known for the model's continuum counterpart. Stability limits in terms of the coupling constants, which depend on the value of the phase-mismatch parameter, are found for solitons of the twisted-mode type in the 1D lattice, and for their counterparts of two different types (one being a discrete vortex) in the 2D lattice. When the twisted-mode soliton is unstable, the instability, which may be either oscillatory or due to imaginary eigenfrequency pairs, transforms the unstable soliton into a stable fundamental one, in both 1D and 2D cases.
authors.affiliation: Department of Inderdisciplinary Studies, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel.
authors.forename: Boris A
authors.initials: BA
authors.lastname: Malomed
authors.forename: P G
authors.initials: PG
authors.lastname: Kevrekidis
authors.forename: D J
authors.initials: DJ
authors.lastname: Frantzeskakis
authors.forename: H E
authors.initials: HE
authors.lastname: Nistazakis
authors.forename: A N
authors.initials: AN
authors.lastname: Yannacopoulos