Related papers: Dynamics of nonlinear-Schroedinger breathers in a …
The existence of breather type solutions, i.e., periodic in time, exponentially localized in space solutions, is a very unusual feature for continuum, nonlinear wave type equations. Following an earlier work [Comm. Math. Phys. {\bf 302},…
We present an analytical model of integrable turbulence in the focusing nonlinear Schr\"odinger (fNLS) equation, generated by a one-parameter family of finite-band elliptic potentials in the semiclassical limit. We show that the spectrum of…
We consider polarons in models of coupled electronic and vibrational degrees of freedom, in the presence of a soft nonlinear inter-particle potential (Morse potential). In particular, we focus on a a bound state of a polaron with a…
We derive a Hamiltonian version of the ${\cal PT}$-symmetric discrete nonlinear Schr\"{o}dinger equation that describes synchronized dynamics of coupled pendula driven by a periodic movement of their common strings. In the limit of weak…
We derive the two-breather solution of the class I infinitely extended nonlinear Schrodinger equation (NLSE). We present a general form of this multi-parameter solution that includes infinitely many free parameters of the equation and free…
Breathers have been experimentally and theoretically found in many physical systems -- in particular, in integrable nonlinear-wave models. A relevant problem is to study the \textit{breather gas}, which is the limit, for $N\rightarrow…
This work focuses on the study of time-periodic solutions, including breathers, in a nonlinear lattice consisting of elements whose contacts alternate between strain-hardening and strain-softening. The existence, stability, and bifurcation…
The quantum sine-Gordon model is the simplest massive interacting integrable quantum field theory whose two-particle scattering matrix is generally non-diagonal. As such, it is a model that has been extensively studied, especially in the…
We show that the parity-time (PT) symmetric coupled optical waveguides with gain and loss support localised oscillatory structures similar to the breathers of the classical $\phi^4$ model. The power carried by the PT-breather oscillates…
We consider the \emph{focusing} nonlinear Schr\"odinger equation posed on the one dimensional line, with nonzero background condition at spatial infinity, given by a homogeneous plane wave. For this problem of physical interest, we study…
Nonlinear classical Hamiltonian lattices exhibit generic solutions in the form of discrete breathers. These solutions are time-periodic and (typically exponentially) localized in space. The lattices exhibit discrete translational symmetry.…
We present a family of discrete breathers, which exists in a nonlinear polarizability model of ferroelectric materials. The core-shell model is set up in its non-dimensionalized Hamiltonian form and its linear spectrum is examined.…
Breathers may be mobile close to an instability threshold where the frequency of a pinning mode vanishes. The translation mode is a marginal mode that is a solution of the linearized (Hill) equation of the breather which grows linearly in…
In an extensive numerical investigation of nonintegrable translational motion of discrete breathers in nonlinear Schrodinger lattices, we have used a regularized Newton algorithm to continue these solutions from the limit of the integrable…
Soliton motion in some external potentials is studied using the nonlinear Schr\"odinger equation. Solitons are scattered by a potential wall. Solitons propagate almost freely or are trapped in a periodic potential. The critical kinetic…
Solitons confined in a channel are studied in the two-dimensional nonlinear Schroedinger equation. When a channel branches into two channels, a soliton is split into two solitons, if the initial kinetic energy exceeds a critical value. The…
Mutual interaction of localized nonlinear waves, e.g. solitons and modulation instability patterns, is a fascinating and intensively-studied topic of nonlinear science. In this research report, we report on the observation of a novel type…
The dynamics of two-component solitons is studied, analytically and numerically, in the framework of a system of coupled extended nonlinear Schr\"odinger equations, which incorporate the cross-phase modulation,…
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…
In this paper we announce the result of asymptotic dynamics of solitons of nonlinear Schrodinger equations with external potentials. To each local minima of the potential there is a soliton centered around it. Under some conditions on the…