Related papers: Mutual transitions between stationary and moving d…
We study spatio-temporal chaos in the complex Ginzburg-Landau equation in parameter regions of weak amplification and viscosity. Turbulent states involving many soliton-like pulses appear in the parameter range, because the complex…
A numerical fluid simulation investigation of the temporal evolution of a special class of traveling wave solution of the one dimensional relativistic cold plasma model is reported.The solutions consist of coupled electromagnetic and plasma…
The traditional picture of heat transfer in solids by atomic vibrations, also known as phonons, involves phonons scattering with each other like gas particles and is commonly referred to as the phonon gas model (PGM). This physical picture…
We study coherent and incoherent interactions between discrete vortex and fundamental solitons in two-dimensional photonic lattices, presenting a new scheme for all-optical routings and topological transformations of vorticities. Due to the…
The main goal of this paper is to understand the formation of hexagonal patterns from the dynamical transition theory point of view. We consider the transitions from a steady state of an abstract nonlinear dissipative system. To shed light…
Using a multiple-scale asymptotic approach, we have derived the complex cubic Ginzburg-Landau equation for amplified and nonlinearly saturated surface plasmon polaritons propagating and diffracting along a metal-dielectric interface. An…
Inspired by Holstein's work on small polaron hopping, the evolution equations of localized states and extended states in presence of atomic vibrations are derived for an amorphous semiconductor. The transition probabilities are obtained for…
Results of numerical simulations of a recently derived most general dissipative-dispersive PDE describing evolution of a film flowing down an inclined plane are presented. They indicate that a novel complex type of spatiotemporal patterns…
In this paper, the unidirectional pulse propagation equation generalized to structured media is derived. A fast modal transform linking the spatio-temporal representation of the field and its modal distribution is presented. This transform…
In this letter we introduce the concept of stabilized vector solitons as nonlinear waves constructed by addition of mutually incoherent Townes solitons that are stabilized under the effect of a periodic modulation of the nonlinearity. We…
We demonstrate that pulses of linear physical systems, weakly perturbed by nonlinear dissipation, exhibit soliton-like behavior in fast collisions. The behavior is demonstrated for linear waveguides with weak cubic loss and for systems…
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…
Pulsating behavior is a universal phenomenon in versatile fields. In nonlinear dissipative systems, the solitons could also pulsate under proper conditions and show many interesting dynamics. However, the pulsation dynamics is generally…
Localized traveling-wave pulses and holes, i.e. localized regions of vanishing wave amplitude, are investigated in a real Ginzburg-Landau equation coupled to a long-wave mode. In certain parameter regimes the pulses exhibit a Hopf…
The analytical theory of chirped dissipative soliton solutions of nonlinear complex Ginzburg-Landau equation is exposed. Obtained approximate solutions are easily traceable within an extremely broad range of the equation parameters and…
We develop a two-dimensional stochastic dissipative theory for the description of the transport of exciton polaritons accounting for their interaction with the environment of acoustic phonons. Our approach is based on the explicit modeling…
We study the waves at the interface between two thin horizontal layers of immiscible fluids subject to high-frequency horizontal vibrations. Previously, the variational principle for energy functional, which can be adopted for treatment of…
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…
Dissipative solitons are remarkable localized states of a physical system that arise from the dynamical balance between nonlinearity, dispersion and environmental energy exchange. They are the most universal form of soliton that can exist…
Clouds of cold neutral atoms driven by a coherent light beam in a ring cavity exhibit self-structured states transversely with respect to the beam axis due to optomechanical forces and the back action of the atomic structures on the beam.…