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Solitons in the Salerno model with competing nonlinearities

AutorGómez-Gardeñes, Jesús; Malomed, B. A.; Floría, Luis Mario; Bishop, A. R.
Fecha de publicación14-mar-2006
EditorAmerican Physical Society
CitaciónPhysical Review E 73: 036608 (2006)
ResumenWe 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.
Descripción8 pages, 10 figures.
Versión del editorhttp://dx.doi.org/10.1103/PhysRevE.73.036608
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