斑图形成与孤子

We analyze the dynamics of two coupled identical populations of quadratic integrate-and-fire neurons, which represent the canonical model for class I neurons near the spiking threshold. The populations are heterogeneous; they include both…

In this work, we have studied the peregrine rogue wave dynamics, with a solitons on finite background (SFB) ansatz, in the recently proposed (Phys. Rev. Lett. 110 (2013) 064105) continuous nonlinear Schrodinger system with parity-time…

We study nonlinear wave phenomena in coupled ring resonator optical waveguides in the tight coupling regime. A discrete model for the system dynamics is put forward and its steady state nonlinear Bloch modes are derived. The switching…

We investigate the spatiotemporal dynamics of cavity solitons in a broad area vertical-cavity surface-emitting laser with saturable absorption subjected to time-delayed optical feedback. Using a combination of analytical, numerical and path…

We report on the dynamics of localized structures in an inhomogeneous Swift-Hohenberg model describing pattern formation in the transverse plane of an optical cavity. This real order parameter equation is valid close to the second order…

Rogue waves named by oceanographers are ubiquitous in nature and appear in a variety of different contexts such as water waves, liquid Helium, nonlinear optics, microwave cavities, etc. In this letter, we propose a novel type of exact…

Quantum fluids of light are an emerging tool employed in quantum many-body physics. Their amazing properties and versatility allow using them in a wide variety of fields including gravitation, quantum information and simulation. However the…

We consider a Boussinesq system describing one-dimensional internal waves which develop at the boundary between two immiscible fluids, and we restrict to its traveling waves. The method which yields explicitly all the elliptic or degenerate…

Under investigation in this paper is the nonisospectral and variable coefficients modified Kortweg-de Vries (vc-mKdV) equation, which manifests in diverse areas of physics such as fluid dynamics, ion acoustic solitons and plasma mechanics.…

With the nonuniform media taken into account, the nonisospectral and variable-coefficient Korteweg-de Vries equation, which describes various physical situations such as fluid dynamics and plasma, is under investigation in this paper. With…

Evidence is presented of universal behavior in modulationally unstable media. An ensemble of nonlinear evolution equations, including three partial differential equations, an integro-differential equation, a nonlocal system and a…

Several methods exist for finding ground (as well as excited) states of nonlinear waves equations. In this paper we first introduce two modifications of the so-called accelerated imaginary-time evolution method (AITEM). In our first…

The Hirota equation is a higher order extension of the nonlinear Schroedinger equation by incorporating third order dispersion and one form of self steepening effect. New periodic waves for the discrete Hirota equation are given in terms of…

In the present work, we examine the potential robustness of extreme wave events associated with large amplitude fluctuations of the Peregrine soliton type, upon departure from the integrable analogue of the discrete nonlinear Schr\"odinger…

The possibility of tailoring the guidance properties of optical fibers along the same direction as the evolution of the optical field allows to explore new directions in nonlinear fiber optics. The new degree of freedom offered by…

This work builds upon the recent demonstration of a phononic four-wave mixing (FWM) pathway mediated by parametric resonance. In such a process, drive tones f_d1 and f_d2 associated with a specific phonon mode interact such that one of the…

We derive the complex Ginzburg-Landau equation for the dynamical self-diffraction of optical waves in a nonlinear cavity. The case of the reflection geometry of wave interaction as well as a medium that possesses the cubic nonlinearity…

In evolution equations for a complex amplitude, the phase obeys a much more intricate equation than the amplitude. Nevertheless, general methods should be applicable to both variables. On the example of the traveling wave reduction of the…

In order to later find explicit analytic solutions, we investigate the singularity structure of a fundamental model of nonlinear optics, the four-wave mixing model in one space variable z. This structure is quite similar, and this is not a…

In the present work, we explore the potential of spin-orbit (SO) coupled Bose-Einstein condensates to support multi-component solitonic states in the form of dark-bright (DB) solitons. In the case where Raman linear coupling between…