2006/03/14 by Jesús Gómez‐Gardeñes, J. Gomez-Gardenes, B. A. Malomed +4 · 1 citation
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Computation #Eigenvalues and eigenvectors #Lattice (music) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Peakon #Physics #Quantum mechanics #Soliton #cond-mat.soft #nlin.PS
paper · pdf · doi:10.1103/physreve.73.036608
published as Physical Review E 73 036608 (2006) · 8 pages, 10 figures
openalex publication_date 2006/03/14 · arxiv created 2006/03/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider a lattice equation (Salerno model) combining onsite self-focusing and intersite self-defocusing cubic terms, which may describe a Bose-Einstein condensate of dipolar atoms trapped in a strong periodic potential. In the continuum approximation, the model gives rise to solitons in a finite band of frequencies, with sechlike solitons near one edge, and an exact peakon solution at the other. A similar family of solitons is found in the discrete system, including a peakon; beyond the peakon, the family continues in the form of cuspons. Stability of the lattice solitons is explored through computation of eigenvalues for small perturbations, and by direct simulations. A small part of the family is unstable (in that case, the discrete solitons transform into robust pulsonic excitations); both peakons and cuspons are stable. The Vakhitov-Kolokolov criterion precisely explains the stability of regular solitons and peakons, but does not apply to cuspons. In-phase and out-of-phase bound states of solitons are also constructed. They exchange their stability at a point where the bound solitons are peakons. Mobile solitons, composed of a moving core and background, exist up to a critical value of the strength of the self-defocusing intersite nonlinearity. Colliding solitons always merge into a single pulse.