Adsorption of a random heteropolymer with self-interactions onto an interface

We consider the adsorption of a random heteropolymer onto an interface within the model by Garel et al. [1] by taking into account self-interactions between the monomers. Within the replica trick and by using a self-consistent preaveraging procedure we map the adsorption problem onto the problem of binding state of a quantum mechanical Hamiltonian. The analysis of the latter is treated within the variational method based on the 2-nd Legendre transform. We have found that self-interactions favor the localization. The effect is intensified with decrease of the temperature. Within a model without taking into account the repulsive ternary monomer-monomer interactions we predict a reentrant localization transition for large values of the asymmetry of the heteropolymer and at low enough temperatures.Comment: 11 pages, 3 figure

Scattering of gap solitons by PT-symmetric defects

The resonant scattering of gap solitons (GS) of the periodic nonlinear Schr\"odinger equation with a localized defect which is symmetric under the parity and the time-reversal (PT) symmetry, is investigated. It is shown that for suitable amplitudes ratios of the real and imaginary parts of the defect potential the resonant transmission of the GS through the defect becomes possible. The resonances occur for potential parameters which allow the existence of localized defect modes with the same energy and norm of the incoming GS. Scattering properties of GSs of different band-gaps with effective masses of opposite sign are investigated. The possibility of unidirectional transmission and blockage of GSs by PT defect, as well as, amplification and destruction induced by multiple reflections from two PT defects, are also discussed

Dynamical generation of interwoven soliton trains by nonlinear emission in binary Bose-Einstein condensates

We propose a method for the generation of trains of alternating bright solitons in two-component Bose-Einstein condensates, using controlled emission of nonlinear matter-waves in the uncoupled regime with spatially-varying intra-species interaction and out-of-phase oscillations of the ground states in the trap. Under this scheme, solitons are sequentially launched from the different components, and interact with each other through phase-independent cross-coupling. We obtain an analytical estimation of the critical condition for soliton emission using a geometric guiding model, in analogy with integrated optical systems. In addition, we show how strong initial perturbations in the system can trigger the spontaneous generation of supersolitons, i.e. localized phonon-like excitations of the soliton trains. Finally, we demonstrate the controllable generation of slow and fast supersolitons by adding external localized potentials in the nonlinear region

Dragging two-dimensional discrete solitons by moving linear defects

We study the mobility of small-amplitude solitons attached to moving defects which drag the solitons across a two-dimensional (2D) discrete nonlinear-Schr\"{o}dinger (DNLS) lattice. Findings are compared to the situation when a free small-amplitude 2D discrete soliton is kicked in the uniform lattice. In agreement with previously known results, after a period of transient motion the free soliton transforms into a localized mode pinned by the Peierls-Nabarro potential, irrespective of the initial velocity. However, the soliton attached to the moving defect can be dragged over an indefinitely long distance (including routes with abrupt turns and circular trajectories) virtually without losses, provided that the dragging velocity is smaller than a certain critical value. Collisions between solitons dragged by two defects in opposite directions are studied too. If the velocity is small enough, the collision leads to a spontaneous symmetry breaking, featuring fusion of two solitons into a single one, which remains attached to either of the two defects

Dynamics of matter solitons in weakly modulated optical lattices

It is shown that matter solitons can be effectively managed by means of smooth variations of parameters of optical lattices in which the condensate is loaded. The phenomenon is based on the effect of lattice modulations on the carrier wave transporting the soliton and that is why is well understood in terms of the effective mass approach, where a particular spatial configuration of the band structure is of primary importance. Linear, parabolic, and spatially localized modulations are considered as the case examples. It is shown that these defects can originate accelerating and oscillating motion of matter solitons as well as simulate soliton interaction with attractive and repulsive defects.Comment: 6 pages, 7 figures (text with major revision