Related papers: Solitons in a medium with linear dissipation and l…
The dynamics of fronts, or kinks, in dispersive media with gain and losses is considered. It is shown that the front parameters, such as the velocity and width, depend on initial conditions. This result is not typical for dissipative…
We introduce a system with one or two amplified nonlinear sites ("hot spots", HSs) embedded into a two-dimensional linear lossy lattice. The system describes an array of evanescently coupled optical or plasmonic waveguides, with gain…
The problem of stability and spectrum of linear excitations of a soliton (kink) of the dispersive sine-Gordon and $\varphi^4$ - equations is solved exactly. It is shown that the total spectrum consists of a discrete set of frequencies of…
We introduce a discrete linear lossy system with an embedded "hot spot" (HS), i.e., a site carrying linear gain and complex cubic nonlinearity. The system can be used to model an array of optical or plasmonic waveguides, where selective…
We consider an array of double oligomers in an optical waveguide device. A mathematical model for the system is the coupled discrete nonlinear Schr\"odinger (NLS) equations, where the gain-and-loss parameter contributes to the…
We predict the existence of surface dark solitons at the interface between a self-defocusing nonlocal nonlinear medium and a linear medium. The fundamental and higher-order surface dark solitons can exist when the linear refractive index of…
Dissipative solitons rely on the double balance between nonlinearity and dispersion as well as gain and loss have attracted a lot of attention in optics, since it gives rise to ultrashort pulses and broadband frequency combs with good…
Propagating intrinsic localised modes (discrete breathers) exist in the dissipative driven sine-Gordon chain as attractors of the dynamics. Thermal fluctuations induce random transitions between attracting configurations corresponding to…
Dissipative solitons are self-localized structures resulting from a double balance between dispersion and nonlinearity as well as dissipation and a driving force. They occur in a wide variety of fields ranging from optics, hydrodynamics to…
We predict the existence of a new type of spatiotemporal solitons ("light bullets") in two-dimensional self-induced-transparency media with refractive index modulation in the direction transverse to that of pulse propagation. These…
We investigate bright matter-wave solitons in the presence of a spatially varying nonlinearity. It is demonstrated that a translation mode is excited due to the spatial inhomogeneity and its frequency is derived analytically and also…
We review the properties of nonlinear, multidimensional localized waves whose stationary propagation is sustained by a dynamic equilibrium between self-focusing and nonlinear losses. Their finite-energy versions preserve light bullet…
We introduce a new concept for stable spatial soliton formation, mediated by the competition between self-bending induced by a strongly asymmetric nonlocal nonlinearity and spatially localized gain superimposed on a wide pedestal with…
We study the surface modes of a homogeneous spherical gain medium and provide a comprehensive analytic treatment of a special class of these modes that support spectral singularities. Because the latter have a divergent quality factor, we…
The existence and stability of the nonlinear spatial localized modes are investigated in parity-time symmetric optical media characterized by a generic complex hyperbolic refractive index distribution with competing gain and loss profile.…
We address the existence and properties of solitons in thermal media with periodic modulation of linear refractive index. Many kinds of solitons in such optical lattices, including symmetric and antisymmetric lattices, are found under…
We demonstrate that the cubic gain applied in a localized region, which is embedded into a bulk waveguide with the cubic-quintic nonlinearity and uniform linear losses, supports stable spatial solitons in the absence of the quintic…
We study solitons in the condensate trapped in a double-well potential with far-separated wells, when the s-wave scattering length has different signs in the two parts of the condensate. By employing the coupled-mode approximation it is…
We study the behavior of the soliton which, while moving in non-dissipative medium encounters a barrier with finite dissipation. The modelling included the case of a finite dissipative layer similar to a wave passing through the…
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…