Related papers: Dragging two-dimensional discrete solitons by movi…
We study the collision of two fast solitons for the nonlinear Schr\"odinger equation in the presence of a spatially adiabatic external potential. For a high initial relative speed $\|v\|$ of the solitons, we show that, up to times of order…
The formation of unstaggered localized modes in dynamical lattices can be supported by the interplay of discreteness and nonlinearity with a finite relaxation time. In rapidly responding nonlinear media, on-site discrete solitons are…
We consider a tracer particle performing a random walk on a two-dimensional lattice in the presence of immobile hard obstacles. Starting from equilibrium, a constant force pulling on the particle is switched on, driving the system to a new…
Dark solitons and localized defect modes against periodic backgrounds are considered in arrays of waveguides with defocusing Kerr nonlinearity constituting a nonlinear lattice. Bright defect modes are supported by local increase of the…
We model discrete spatial solitons in a periodic nonlinear medium encompassing any degree of transverse non locality. Making a convenient reference to a widely used material -nematic liquid crystals-, we derive a new form of the discrete…
Solitons are localised wave disturbances that propagate without changing shape, a result of a nonlinear interaction which compensates for wave packet dispersion. Individual solitons may collide, but a defining feature is that they pass…
In this paper we study dynamics of solitons in the generalized nonlinear Schr\"odinger equation (NLS) with an external potential in all dimensions except for 2. For a certain class of nonlinearities such an equation has solutions which are…
We study the integrable nonlocal nonlinear Schr\"odinger equation proposed by Ablowitz and Musslimani, that is considered as a particular example of equations with parity-time ($\mathcal{PT}$) symmetric self-induced potential. We consider…
Electric field induced collective reorientation of nematic molecules placed between two flat parallel electrodes is of importance for both fundamental science and practical applications. This reorientation is either homogeneous over the…
We consider a one-dimensional discrete nonlinear Schr{\"o}dinger (dNLS) model featuring interactions beyond nearest neighbors. We are interested in the existence (or nonexistence) of phase-shift discrete solitons, which correspond to…
We investigate dynamical aspects of the discrete nonlinear Schr\"{o}dinger equation (DNLS) in finite lattices. Starting from a periodic chain with nearest neighbor interactions, we insert randomly links connecting distant pairs of sites…
We demonstrate that the commonly known concept, which treats solitons as nonsingular solutions produced by the interplay of nonlinear self-attraction and linear dispersion, may be extended to include modes with a relatively weak singularity…
Onset of permanent deformation in crystalline materials under a sharp indenter tip is accompanied by nucleation and propagation of defects. By measuring the spatio-temporal strain field nearthe indenter tip during indentation tests, we…
We study the amplitude dynamics of two-dimensional (2D) solitons in a fast collision described by the coupled nonlinear Schr\"odinger equations with a saturable nonlinearity and weak nonlinear loss. We extend the perturbative technique for…
It was recently proved that isolated unstable "embedded lattice solitons" (ELS) may exist in discrete systems. The discovery of these ELS gives rise to relevant questions such as the following: are there continuous families of ELS?, can ELS…
In this work, we study long-time wave transport in correlated and uncorrelated disordered 2D arrays. When a separation of dimensions is applied to the model, we find that the predicted 1D random dimer phenomenology also appears in so-called…
We examine one- and two-dimensional (1D and 2D) models of linearly coupled lattices of the discrete-nonlinear-Schr{\"{o}}dinger type. Analyzing ground states of the systems with equal powers in the two components, we find a…
We integrate the one-dimensional nonlinear Schr\"odinger equation numerically for solitons moving in external potentials. In particular, we study the scattering off an interface separating two regions of constant potential modeled by a…
In this paper, we employ a combination of analytical and numerical techniques to investigate the dynamics of lattice envelope vector soliton solutions propagating within a one-dimensional chain of flexible mechanical metamaterial. To model…
Considering a two-dimensional Bose-Hubbard spinor lattice with weak nearest neighbour interactions and no particle transfer between sites, we theoretically study the transport of energy from one initially excited dimer, to the rest of the…