斑图形成与孤子

We prove the existence of time-periodic solutions consisting of patterns built up from two states, one with small amplitude and the other one with large amplitude, in general nonlinear Hamiltonian finite-size lattices with global coupling.…

We continue the discussion on the interaction energy of the axially symmetric Hopfions evaluated directly from the product anzsatz. The Hopfions are given by the projection of Skyrme model solutions onto the coset space SU(2)/U(1). Our…

The effect of shear flow on mode selection and the length scale of patterns formed in a nonlinear auto-catalytic reaction-diffusion model is investigated. We predict analytically the existence of transverse and longitudinal modes. The type…

We find that diverse nonlinear waves, such as soliton, Akhmediev breather, and rogue waves (RWs), can emerge and interplay with each other in a two-mode coupled system. It provides a good platform to study interaction between different…

We investigate the formation of localized structures with a varying width in one and two-dimensional systems. The mechanism of stabilization is attributed to strong nonlocal coupling mediated by a Lorentzian type of Kernel. We show that, in…

We study dynamical response of a nonlinear dimer to a symmetrically injected monochromatic wave. We find a domain in the space of frequency and amplitude of the injected wave where all stationary solutions are unstable. In this domain…

We show that the onset of laser multiple filamentation can be described as a critical phenomenon that we characterize both experimentally and numerically by measuring a set of seven critical exponents. This phase transition deviates from…

Chimera states consisting of domains of coherently and incoherently oscillating nonlocally-coupled phase oscillators in systems with spatial inhomogeneity are studied. The inhomogeneity is introduced through the dependence of the oscillator…

Both low frequency and high frequency impurity modes have been produced in a SiN micromechanical cantilever array by illumination with either an infrared or visible laser. When such laser-induced impurities are placed near a driven…

In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as Mass-in-Mass systems. We use 3 distinct approaches to identify relevant traveling waves. The first consists of…

We consider a two-dimensional (2D) generalization of a recently proposed model [Phys. Rev. E 88, 032905 (2013)], which gives rise to bright discrete solitons supported by the defocusing nonlinearity whose local strength grows from the…

In the present work, we theoretically propose and numerically illustrate a mean-field analogue of the Hong-Ou-Mandel experiment with bright solitons. More specifically, we scatter two solitons off of each other (in our setup, the bright…

Toroidal modes in the form of so-called Hopfions, with two independent winding numbers, a hidden one (twist, s), which characterizes a circular vortex thread embedded into a three-dimensional soliton, and the vorticity around the vertical…

We consider the effects of a Mexican-hat-shaped nonlocal spatial coupling, i.e., symmetric long-range inhibition superimposed with short-range excitation, upon front propagation in a model of a bistable reaction-diffusion system. We show…

We report a new mechanism of pattern formation in growing bistable systems coupled indirectly. A modified Fujita et. al. model is studied as an example of a reaction-diffusion system of nondiffusive activator and inhibitor molecules…

State transition between the Peregrine rogue wave and w-shaped traveling wave induced by higher-order effects and background frequency is studied. We find that this intriguing transition, described by an exact explicit rational solution, is…

The nonlinear nonlocal Michelson-Sivashinsky equation for isolated crests of unstable flames is studied, using pole-decompositions as starting point. Polynomials encoding the numerically computed 2N flame-slope poles, and auxiliary ones,…

Symmetry breaking is reported for continuous families of solitons in the nonlinear Schr\"odinger equation with a two-dimensional complex potential. This symmetry-breaking bifurcation is forbidden in generic complex potentials. However, for…

We apply the variational approach to solitons in highly nonlocal nonlinear media in $D=1,2,3$ dimensions. We compare results obtained by the variational approach with those obtained in the accessible soliton approximation, by considering…

Inspired by the experimental results of Cuevas et al. (Physical Review Letters 102, 224101 (2009)), we consider theoretically the behavior of a chain of planar rigid pendulums suspended in a uniform gravitational field and subjected to a…