title: Solitons in the Salerno model with competing nonlinearities.
abstract: 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.
authors.affiliation: Departamento de Física de la Materia Condensada and Instituto de Biocomputación y Física de los Sistemas Complejos, Universidad de Zaragoza, E-50009 Zaragoza, Spain.
authors.forename: J
authors.initials: J
authors.lastname: Gomez-Gardeñes
authors.forename: B A
authors.initials: BA
authors.lastname: Malomed
authors.forename: L M
authors.initials: LM
authors.lastname: Floría
authors.forename: A R
authors.initials: AR
authors.lastname: Bishop