斑图形成与孤子
The breather solution found by M. Tajiri and Y. Murakami for the Boussinesq equation is studied analytically. The new parameterization of the solution is proposed, allowing us to find exactly the existence boundary of the Boussinesq…
We present an experimental and theoretical study of the effect of spatio-temporal fluctuations in quasi-reversible systems displaying a spatial quintic supercritical bifurcation. The saturation mechanism is drastically changed by the…
The nonlocal nonlinear evolution equations describe phenomena in which wave evolution is influenced by local and nonlocal spatial and temporal variables. These equations have opened up a new wave of physically important nonlinear evolution…
Stability is an essential problem in theoretical and experimental studies of solitons in nonlinear media with fractional diffraction, which is represented by the Riesz derivative with Levy index (LI) taking values LI < 2. Fractional…
Kinks (or domain walls) are localized transitions between distinct ground states associated with a topological invariant, and are central to many phenomena across physics, from condensed matter to cosmology. While phonon (i.e.,…
Thouless pumps are time-periodic one-dimensional systems that capture the physics of the two-dimensional quantum Hall effect via the quantized pumping of particles under adiabatic modulation. Recent work in photonics has shown that…
In this work, we study a prototypical, experimentally accessible scenario that enables the systematic generation of so-called high-order rogue waves in atomic Bose-Einstein condensates. These waveforms lead to significantly and controllably…
We study the matter-wave solitons in Bose-Einstein condensate (BEC) trapped on a M\"{o}bius strip (MS), based on the respective Gross-Pitaevskii (GP) equation with the mean-field theory. In the linear regime, vortex states are characterized…
We study the propagation of a domain wall (kink) of the $\phi^4$ model in a radially symmetric environment defined by a gravity source. This source deforms the standard Euclidian metric into a Schwarzschild-like one. We introduce an…
The behavior of the kink in the sine-Gordon (sG) model in the presence of periodic inhomogeneity is studied. An ansatz is proposed that allows for the construction of a reliable effective model with two degrees of freedom. Effective models…
In the present work we explore the interaction of a one-dimensional kink-like front of the sine-Gordon equation moving in 2-dimensional spatial domains. We develop an effective equation describing the kink motion, characterizing its center…
In the present study the interaction of a sine-Gordon kink with a localized inhomogeneity is considered. In the absence of dissipation, the inhomogeneity considered is found to impose a potential energy barrier. The motion of the kink for…
Thermal noise and harmonic forcing have recently been shown to cooperatively excite sine-Gordon breathers robust to dissipation. Such a phenomenon has been found assuming a Gaussian noise source, delta-correlated both in time and space. In…
Thin films or sheets subjected to external forces often undergo mechanical instability, leading to regular patterns of wrinkles, folds, and creases. As can be anticipated from the difficulty of flattening a curved globe, any natural…
We investigate the emergence of induced localized coupled modes in passive cavities with both loss and gain. Our model is based on linearly coupled Lugiato-Lefever equations, where a Gaussian pump beam is applied to only one mode. Through…
Recent studies have shown that a soliton can be {\it fractionally} transported by slowly varying a system parameter over one period in a nonlinear system. This phenomenon is attributed to the nontrivial topology of the corresponding energy…
We discuss some aspects of numerical continuation and bifurcation for partial differential equations, specifically pattern formation and coherent structures. For the sake of clarity we focus on wavetrains, stability and associated invasion…
Travelling-wave, quasi-periodic and ``longulent'' states of the Galerkin-regularized systems preserving finite Fourier modes are exposed. The longulent states are characterized by solitonic structures, called ``longons'', accompanied by…
In this paper, we propose a general mechanism for the existence of quasicrystals in spatially extended systems (partial differential equations with Euclidean symmetry). We argue that the existence of quasicrystals with higher order…
We investigate time-independent solutions of a discrete optical cavity model featuring saturable Kerr nonlinearity, a discrete version of the Lugiato-Lefever equation. This model supports continuous wave (uniform) and localized (discrete…