English
Related papers

Related papers: Solitons in coupled Ablowitz-Ladik chains

200 papers

In the present work, we propose a new set of coherent structures that arise in nonlinear dynamical lattices with more than one components, namely interlaced solitons. These are waveforms in which in the relevant anti-continuum limit, i.e.…

Pattern Formation and Solitons · Physics 2015-05-20 J. Cuevas , Q. E. Hoq , H. Susanto , P. G. Kevrekidis

It is well known that the two-dimensional (2D) nonlinear Schr\"odinger equation (NLSE) with the cubic-quintic (CQ) nonlinearity supports a family of stable fundamental solitons, as well as solitary vortices (alias vortex rings), which are…

Pattern Formation and Solitons · Physics 2015-05-20 Nir Dror , Boris A. Malomed

A modification of the usual Type-II second-harmonic-generation model is proposed, which includes two additional features: linear conversion and walkoff (group-velocity difference) between two components of the fundamental-frequency (FF)…

Pattern Formation and Solitons · Physics 2009-11-07 Arkady Kaplan , Boris A. Malomed

We introduce four basic two-dimensional (2D) plaquette configurations with onsite cubic nonlinearities, which may be used as building blocks for 2D PT -symmetric lattices. For each configuration, we develop a dynamical model and examine its…

Quantum Physics · Physics 2012-10-24 Kai Li , P. G. Kevrekidis , Boris A. Malomed , Uwe Guenther

The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and…

Pattern Formation and Solitons · Physics 2009-11-11 I. Kourakis , P. K. Shukla

A model of the optical media with a spatially structured Kerr nonlinearity is introduced. The nonlinearity strength is modulated by a set of singular peaks on top of a self-focusing or defocusing uniform background. The peaks may include a…

Optics · Physics 2017-06-28 Vitaly Lutsky , Boris A. Malomed

The existence and stability of defect solitons supported by parity-time (PT) symmetric superlattices with nonlocal nonlinearity are investigated. In the semi-infinite gap, in-phase solitons are found to exist stably for positive or zero…

Optics · Physics 2012-04-17 Sumei Hu , Daquan Lu , Xuekai Ma , Qi Guo , Wei Hu

An integrable discretization of the inhomogeneous Ablowitz-Ladik model with a linear force is introduced. Conditions on parameters of the discretization which are necessary for reproducing Bloch oscillations are obtained. In particular, it…

solv-int · Physics 2009-10-31 V. V. Konotop

We study soliton dynamics in a system of two linearly coupled discrete nonlinear Schr\"odinger equations, which describe the dynamics of a two-component Bose gas, coupled by an electromagnetic field, and confined in a strong optical…

Pattern Formation and Solitons · Physics 2009-04-20 A. Trombettoni , H. E. Nistazakis , Z. Rapti , D. J. Frantzeskakis , P. G. Kevrekidis

Dynamics of a chain of interacting parity-time invariant nonlinear dimers is investigated. A dimer is built as a pair of coupled elements with equal gain and loss. A relation between stationary soliton solutions of the model and solitons of…

This paper reviews theoretical advances on the formation and stabilization of multidimensional solitons in nonlinear Schr\"odinger systems with attractive interactions, focusing on atomic Bose-Einstein condensates and nonlinear optics.…

Quantum Gases · Physics 2026-03-31 Fatkhulla Abdullaev , Mario Salerno

We consider a long fiber-optical link consisting of alternating dispersive and nonlinear segments, i.e., a split-step model (SSM), in which the dispersion and nonlinearity are completely separated. Passage of a soliton through one cell of…

Pattern Formation and Solitons · Physics 2007-05-23 Rodislav Driben , Boris A. Malomed

The existence and stability of defect solitons in parity-time (PT) symmetric optical lattices with nonlocal nonlinearity are reported. It is found that nonlocality can expand the stability region of defect solitons. For positive or zero…

Optics · Physics 2012-04-19 Sumei Hu , Xuekai Ma , Daquan Lu , Yizhou Zheng , Wei Hu

It is shown that the pair plasmas with small temperature asymmetry can support existence of localized as well as de-localized optical vortex solitons. Coexistence of such solitons is possible due to peculiar form of saturating nonlinearity…

Plasma Physics · Physics 2013-05-29 V. I. Berezhiani , S. M. Mahajan , N. L. Shatashvili

The dynamics of two active nonlinear resonators coupled to a linear resonator is studied theoretically. Possible stationary states and its dynamical stability are considered in detail. The spontaneous symmetry breaking is found and it is…

Optics · Physics 2022-04-06 D. Dolinina , A. Yulin

We consider the discrete solitons bifurcating from the anti-continuum limit of the discrete nonlinear Schr\"{o}dinger (NLS) lattice. The discrete soliton in the anti-continuum limit represents an arbitrary finite superposition of {\em…

Pattern Formation and Solitons · Physics 2007-05-23 D. E. Pelinovsky , P. G. Kevrekidis , D. J. Frantzeskakis

Since the parity-time-(PT-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with PT-symmetric potentials have been investigated. However, previous studies of PT-symmetric waves were…

Pattern Formation and Solitons · Physics 2017-05-29 Yong Chen , Zhenya Yan , Dumitru Mihalache , Boris A. Malomed

The parametrically driven damped nonlinear Schr\"odinger equation serves as an amplitude equation for a variety of resonantly forced oscillatory systems on the plane. In this note, we consider its nodal soliton solutions. We show that…

Pattern Formation and Solitons · Physics 2007-05-23 N. V. Alexeeva , E. V. Zemlyanaya

Two-dimensional (2D) fundamental soliton-soliton pairs are investigated in binary mixtures of Bose-Einstein condensates with attractive interactions between atoms of the same type. Both attractive and repulsive interactions between atoms of…

Pattern Formation and Solitons · Physics 2012-03-16 A. I. Yakimenko , K. O. Shchebetovska , S. I. Vilchinskii , M. Weyrauch

We investigate soliton mobility in the disordered Ablowitz-Ladik (AL) model and the standard nonlinear Schr\"{o}dinger (NLS) lattice with the help of an effective potential generalizing the Peierls-Nabarro potential. This potential results…

Pattern Formation and Solitons · Physics 2015-09-04 Zhi-Yuan Sun , Shmuel Fishman , Avy Soffer