2006/07/04 by Hidetsugu Sakaguchi, Boris A. Malomed · 1 citation
Physics and Astronomy · #Breather #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Lattice (music) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Optical lattice #Optical vortex #Periodic potential #Physics #Quantum mechanics #Quasiperiodic function #cond-mat.soft #cond-mat.stat-mech #nlin.PS
paper · pdf · doi:10.1103/physreve.74.026601
8 pages, 11 figures
arxiv created 2006/07/04 · openalex publication_date 2006/08/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.