Related papers: Bright Discrete Solitons in Spatially Modulated DN…
We overview the properties of nonlinear guided waves and (bright and dark) spatial optical solitons in a periodic medium created by a sequence of linear and nonlinear layers. First, we consider a single layer with a cubic nonlinear response…
Embedded solitons are exceptional modes in nonlinear-wave systems with the propagation constant falling in the system's propagation band. An especially challenging topic is seeking for such modes in nonlinear dynamical lattices (discrete…
Discrete fundamental and dipole solitons are constructed, in an exact analytical form, in an array of linear waveguides with an embedded $\mathcal{PT}$-symmetric dimer, which is composed of two nonlinear waveguides carrying equal gain and…
We review asymptotic stability of solitary waves for nonlinear dispersive equations set on the line. Our focus is threefold: first, the nonlinear Schrodinger equation; second, the notion of full asymptotic stability (which states that…
We consider a modulated discrete nonlinear Schr\"odinger (DNLS) model with alternating on-site potential, having a linear spectrum with two branches separated by a 'forbidden' gap. Nonlinear localized time-periodic solutions with…
We consider modeling for strong-strong beam-beam interactions beyond preceding linearized/perturbative methods such as soft gaussian approximation or FMM (HFMM) etc. In our approach discrete coherent modes, discovered before, and possible…
We characterize the soliton solutions of the nonlinear Schroedinger equation on the half line with linearizable boundary conditions. Using an extension of the solution to the whole line and the corresponding symmetries of the scattering…
In this work we derive evolution equations for the nonlinear behavior of a coasting beam under the influence of a resonator impedance. Using a renormalization group approach we find a set of coupled nonlinear equations for the beam density…
The properties of the localized states of a two component Bose-Einstein condensate confined in a nonlinear periodic potential [nonlinear optical lattice] are investigated. We reveal the existence of new types of solitons and study their…
We report the coexistence and properties of stable compact localized states (CLSs) and discrete solitons (DSs) for nonlinear spinor waves on a flatband network with spin-orbit coupling (SOC). The system can be implemented by means of a…
It is well known that the linear stability of solutions of partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the…
We investigate the existence of spatially localised solutions, in the form of discrete breathers, in general damped and driven nonlinear lattice systems of coupled oscillators. Conditions for the exponential decay of the difference between…
In the present work we revisit the problem of the dark solitary wave pinned in the discrete nonlinear Schr{\"o}dinger equation. In a number of recent studies, the methodology of exponential asymptotics was attempted to be utilized in this…
Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with low-dimensional (1D) conservative plus dissipative nonlinear optical lattices are investigated. In the case of focusing media (with attractive…
We study the point spectrum of the linearization at a solitary wave solution $\phi_\omega(x)e^{-\mathrm{i}\omega t}$ to the nonlinear Dirac equation in $\mathbb{R}^n$, $n\ge 1$, with the nonlinear term given by $f(\psi^*\beta\psi)\beta\psi$…
We construct a class of exact commensurate and incommensurate standing wave (SW) solutions in a piecewise smooth analogue of the discrete non-linear Schr\"{o}dinger (DNLS) model and present their linear stability analysis. In the case of…
We investigate the focusing coupled PT-symmetric nonlocal nonlinear Schrodinger equation employing Darboux transformation approach. We find a family of exact solutions including pairs of Bright-Bright, Dark-Dark and Bright-Dark solitons in…
We examine the spectral properties of single and multiple matter-wave dark solitons in Bose-Einstein condensates confined in parabolic traps, where the scattering length is periodically modulated. In addition to the large-density limit…
We present a comprehensive analytical theory of localized nonlinear excitations - dark solitons, supported by an incoherently pumped, spatially homogeneous exciton-polariton condensate. We show that, in contrast to dark solitons in…
This is a survey on the local structure about a fixed point of discrete finite-dimensional holomorphic dynamical systems, discussing in particular the existence of local topological conjugacies to normal forms, and the structure of local…