斑图形成与孤子

In this paper the effect of a small dissipation on waves is included to find exact solutions to the modified BBM equation. Using Lyapunov functions and dynamical systems theory, we prove that when viscosity is added to the BBM equation, in…

In this work, we revisit a criterion, originally proposed in [Nonlinearity {\bf 17}, 207 (2004)], for the stability of solitary traveling waves in Hamiltonian, infinite-dimensional lattice dynamical systems. We discuss the implications of…

We identify that for a broad range of parameters a variant of the soliton solution of the one-dimensional non-linear Schr\"{odinger} equation, the {\it breather}, is distinct when one studies the associated space curve (or soliton surface),…

Recently for the sine-Gordon equation it has been established that during collisions of $N$ slow kinks maximal energy density increases as $N^2$. In this numerical study, the same scaling rule is established for the non-integrable $\phi^4$…

In this paper, we study the $\phi^4$ kink scattering from a spatially localized $\mathcal{PT}$-symmetric defect and the effect of the kink's internal mode (IM) is discussed. It is demonstrated that if a kink hits the defect from the gain…

Using a variational formulation for partial differential equations (PDEs) combined with numerical simulations on ordinary differential equations (ODEs), we find two categories (pulses and snakes) of dissipative solitons, and analyze the…

Traveling wave solutions to Kawahara equation (KE), transmission line (TL), and Korteweg-de Vries (KdV) equation are found by using an elliptic function method which is more general than the $\mathrm{tanh}$-method. The method works by…

A systematic experimental and numerical investigation of the conditions for the spontaneous formation of laser cavity solitons in broad-area vertical-cavity surface-emitting lasers with frequency-selective feedback by a volume Bragg grating…

We explain the concept of Krein signature in Hamiltonian and $\mathcal{PT}$-symmetric systems on the case study of the one-dimensional Gross-Pitaevskii equation with a real harmonic potential and an imaginary linear potential. These…

We report on the existence of stable, completely delocalized response regimes in a nonlinear defective periodic structure. In this state of complete delocalization, despite the presence of the defect, the system exhibits in-phase…

In the framework of the Gross-Pitaevskii equation, we study the formation and stability of effectively two-dimensional solitons in dipolar Bose-Einstein condensates (BECs), with dipole moments polarized at an arbitrary angle $\theta$…

A systematic approach for deriving tight-binding approximations in general longitudinally driven lattices is presented. As prototypes, honeycomb and staggered square lattices are considered. Time-reversal symmetry is broken by…

The relationship between point vortex dynamics and the properties of polynomials with roots at the vortex positions is discussed. Classical polynomials, such as the Hermite polynomials, have roots that describe the equilibria of identical…

Recent experiments on walking droplets suggest an underlying connection between fluid dynamics and the quantum mechanics. Such experiments may be used to support the de Broglie-Bohm pilot-wave theory. In this paper we show that many…

The article deals with the sin-Gordon model and considers the interaction of breathers localized on moving impurities. Numerical simulation of collective behavior of such objects revealed the analogy between the models properties and the…

Stationary expansion shocks have been recently identified as a new type of solution to hyperbolic conservation laws regularized by non-local dispersive terms that naturally arise in shallow-water theory. These expansion shocks were studied…

In dispersive media, hydrodynamic singularities are resolved by coherent wavetrains known as dispersive shock waves (DSWs). Only dynamically expanding, temporal DSWs are possible in one-dimensional media. The additional degree of freedom…

New two-component soliton solutions of the coupled high-frequency (HF) - low-frequency (LF) system, based on Schr\"odinger - Korteweg - de Vries (KdV) system with the Zakharov's coupling, are obtained for arbitrary relative strengths of the…

Tundra lakes are key components of the Arctic climate system because they represent a source of methane to the atmosphere. In this paper, we aim to analyze the geometry of the patterns formed by large ($>0.8$ km$^2$) tundra lakes in the…

We study the dynamics of an array of nearest-neighbor coupled spatially distributed systems each generating a periodic sequence of short pulses. We demonstrate that unlike a solitary system generating a train of equidistant pulses, an array…