Discrete Solitons in the Salerno Model with competing nonlinearities
| dc.creator | Gomez-Gardenes, J. | |
| dc.creator | Malomed, B. A. | |
| dc.creator | Floria, L. M. | |
| dc.creator | Bishop, A. R. | |
| dc.date | 2006-03-23 | |
| dc.date.accessioned | 2026-07-07T07:07:28Z | |
| dc.date.available | 2026-07-07T07:07:28Z | |
| dc.description | 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. | |
| dc.description | 8 pages, 10 figures | |
| dc.identifier | https://arxiv.org/abs/nlin/0603050 | |
| dc.identifier | http://arxiv.org/abs/nlin/0603050 | |
| dc.identifier | Physical Review E 73 036608 (2006) | |
| dc.identifier | doi:10.1103/PhysRevE.73.036608 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110405 | |
| dc.subject | Pattern Formation and Solitons | |
| dc.subject | Soft Condensed Matter | |
| dc.title | Discrete Solitons in the Salerno Model with competing nonlinearities | |
| dc.type | text |