斑图形成与孤子

We investigate wave mixing effects in a phononic crystal that couples the wave dynamics of two channels -- primary and control ones -- via a variable stiffness mechanism. We demonstrate analytically and numerically that the wave…

Macroscopic systems subjected to injection and dissipation of energy can exhibit complex spatiotemporal behaviors as result of dissipative self-organization. Here, we report a one and two dimensional pattern forming set up, which exhibits a…

We review various methods for the analysis of initial-value problems for integrable dispersive equations in the weak-dispersion or semiclassical regime. Some methods are sufficiently powerful to rigorously explain the generation of…

Original Whitham's method of derivation of modulation equations is applied to systems whose dynamics is described by a perturbed Korteweg-de Vries equation. Two situations are distinguished: (i) the perturbation leads to appearance of…

The localization characters of the first-order rogue wave (RW) solution $u$ of the Kundu-Eckhaus equation is studied in this paper. We discover a full process of the evolution for the contour line with height $c^2+d$ along the orthogonal…

We demonstrate that repulsive power law interactions can induce directed transport of particles in dissipative, ac-driven periodic potentials, in regimes where the underlying noninteracting system exhibits localized oscillations.…

We investigate the formation and stability of icosahedral quasicrytalline structures using a dynamic phase field crystal model. Nonlinear interactions between density waves at two length scales stabilize three-dimensional quasicrystals. We…

We demonstrate numerically the existence of nonlinear Tamm oscillations at the interface between a substrate and one-dimensional waveguide array with both cubic and saturable, self-focusing and self-defocusing nonlinearity. Light is trapped…

We present an unifying description of a new class of localized states, appearing as large amplitude peaks nucleating over a pattern of lower amplitude. Localized states are pinned over a lattice spontaneously generated by the system itself.…

We present a general approach to the study of synchrony in networks of weakly nonlinear systems described by singularly perturbed equations of the type $x''+x+\epsilon f(x,x')=0$. By performing a perturbative calculation based on normal…

We derive a closed equation for the shape of the free surface of a magnetic fluid subject to an external magnetic field. The equation is strongly non-local due to the long range character of the magnetic interaction. We develop a systematic…

Spatio-temporal bifurcations and complex dynamics in globally coupled intrinsically bistable electrochemical systems with an S-shaped current-voltage characteristic under galvanostatic control are studied theoretically on a one-dimensional…

The formation of patterns of peaks on the free surface of a ferrofluid subject to a magnetic field normal to the undisturbed interface is investigated theoretically. The relative stability of ridge, square, and hexagon planforms is studied…

By numerical simulation methods the interactions of oscillating solutions (breathers) of the (2+1)-dimensional O(3) nonlinear sigma model is investigated. The models of head-on collisions in which the interacting breathers, in particular,…

Through three examples we illustrate some of the concepts and ingredients required for pattern formation at mesoscopic scales. Two examples build on microscopic models where mesoscopic patterns emerge from homogeneous ground states driven…

We investigate the impact of the domain shape on wave propagation in excitable media. Channelled domains with sinusoidal boundaries are considered. Trains of fronts generated periodically at an extreme of the channel are found to adopt a…

We consider a two-component, two-dimensional nonlinear Schr\"{o}dinger system with unequal dispersion coefficients and self-defocusing nonlinearities, chiefly with equal strengths of the self- and cross-interactions. In this setting, a…

Stability of the kink-like and soliton-like travelling wave solutions to the generalized convection-reaction-diffusion equation is studied by means of the qualitative methods and numerical simulation.

By methods of numerical simulation the interaction of 180-degree domain walls with oscillating solitons in (2+1)-dimensional O(3) nonlinear sigma model is investigated. A model of the collisions in which there is observed a reflection of…

This paper firstly show that 2 Dimensional Intelligent Driver Model (Jiang et al., PloS one, 9(4), e94351, 2014) is not able to replicate the synchronized traffic flow. Then we propose an improved model by considering the difference between…