title: Gap solitons in quasiperiodic optical lattices.
abstract: Families of solitons in one- and two-dimensional (1D and 2D) Gross-Pitaevskii equations with the repulsive nonlinearity and a potential of the quasicrystallic type are constructed (in the 2D case, the potential corresponds to a fivefold optical lattice). Stable 1D solitons in the weak potential are explicitly found in three band gaps. These solitons are mobile, and they collide elastically. Many species of tightly bound 1D solitons are found in the strong potential, both stable and unstable (unstable ones transform themselves into asymmetric breathers). In the 2D model, families of both fundamental and vortical solitons are found and are shown to be stable.
authors.affiliation: Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan.
authors.forename: Hidetsugu
authors.initials: H
authors.lastname: Sakaguchi
authors.forename: Boris A
authors.initials: BA
authors.lastname: Malomed