斑图形成与孤子

Can a simple oscillator system, as in cellular automata, sustain complex nature upon discretization in time and space? The answer is by no means trivial as even the most simple, two-state, nearest neighbours cellular automata can lead to…

We propose general conditions for the emergence of Turing patterns in a domain that changes size through homogeneous growth/shrinkage based on the qualitative changes of a potential function. For this part of the work, we consider the most…

In this paper, we study data-driven localized wave solutions and parameter discovery in the massive Thirring (MT) model via the deep learning in the framework of physics-informed neural networks (PINNs) algorithm. Abundant data-driven…

We study a class of physically intriguing PT-symmetric generalized Scarf-II (GS-II) potentials, which can support exact solitons in one- and multi-dimensional nonlinear Schr\"odinger equation. In the 1D and multi-D settings, we find that a…

We report on the experimental observation of solitons propagating along a torus of fluid. We show that such a periodic system leads to significant differences compared to the classical plane geometry. In particular, we highlight the…

The generalized nonlinear Schr\"odinger equation with full dispersion (FDNLS) is considered in the semiclassical regime. The Whitham modulation equations are obtained for the FDNLS equation with general linear dispersion and a generalized,…

We study the stability and characteristics of two-dimensional (2D) circular quantum droplets (QDs) with embedded hidden vorticity (HV), i.e., opposite angular momenta in two components, formed by binary Bose-Einstein condensates (BECs)…

Soliton gases represent large random soliton ensembles in physical systems that display integrable dynamics at the leading order. We report hydrodynamic experiments in which we investigate the interaction between two "beams" or "jets" of…

We identify a class of trapping potentials in cubic nonlinear Schr\"{o}dinger equations (NLSEs) that make them non-integrable, but prevent the emergence of power spectra associated with ergodicity. The potentials are characterized by…

The dynamics of solitons driven in a nonlinear Thouless pump and its connection with the system's topology were recently explored for both weak and strong nonlinear strength. This work uncovers the fate of nonlinear Thouless pumping in the…

In this paper we examine the effect of delamination on wave scattering, with the aim of creating a control measure for layered waveguides of various bonding types. Previous works have considered specific widths of solitary waves for the…

The collapse of man-made and natural structures is a complex phenomenon that has been studied for centuries. We propose a new approach to understanding catastrophic instabilities, based on the idea that they do not occur at the critical…

We analyze a spatially extended version of a well-known model of forest-savanna dynamics, which presents as a system of nonlinear partial integro-differential equations, and study necessary conditions for pattern-forming bifurcations.…

We propose conditions for the emergence of Turing patterns in a domain that changes in size by homogeneous growth/shrinkage. These conditions to determine the bifurcation are based on considering the geometric change of a potential function…

The reaction-diffusion processes in a growing domain involves a dilution term that modifies the properties of the homogeneous state that, in contrast to a fixed domain, depends on time. We study how the dilution term changes the steady…

We study theoretically the mechanisms of square wave formation of a vertically emitting micro-cavity operated in the Gires-Tournois regime that contains a Kerr medium and that is subjected to strong time-delayed optical feedback and detuned…

We study the properties of optical pulse in cubic-quintic nonlinear media using information theoretic approach. The system can support regular (sharp top) and flat top pulse depending on the type of quintic interaction and the frequency of…

In this work we report on the emergence of a novel type of solitary waves, viz., time-localized solitons in integrable and non-integrable variants of the massive Thirring models and in the three-wave resonant-interaction system, which are…

In the present work, we study coherent structures in a one-dimensional discrete nonlinear Schr\"odinger lattice in which the coupling between waveguides is periodically modulated. Numerical experiments with single-site initial conditions…

The singularly perturbed Gierer-Meinhardt (GM) system in a bounded $d$-dimensional domain ($d\geq 2$) is known to exhibit boundary layer (BL) solutions for a non-zero activator flux. It was previously shown that such BL solutions can be…