Pattern Formation and Solitons
We investigate the dynamics of vector solitons in a two-component Bose-Einstein condensates governed by the system of Gross-Pitaevskii equations. Using a gauge-transformation approach, we construct a four-soliton solution and analyze their…
A symmetric $\phi^4$-$\phi^2 |\phi|$-$\phi^2$ model has recently attracted a lot of attention due to its usefulness in studying tunable phase transitions. We analyze the behavior of this model for the entire range of parameters and obtain…
We revisit aspects of dynamics and stability of localized states in the deterministic and stochastic discrete nonlinear Schr\"odinger equation. By a combination of analytic and numerical techniques, we show that localized initial conditions…
We investigate the computation of stable fracture paths in brittle thin films using one-dimensional damage models with an elastic foundation. The underlying variational formulation is non-convex, making the evolution path sensitive to…
We introduce a model governing the copropagation of two components which represent circular polarizations of light in the optical fiber with relative strength g = 2 of the nonlinear repulsion between the components, and linear coupling…
We study nonlinear excitations described by DNLS-type equations with so-called competing nonlinearities. These are the nonlinearities that consist of two power terms with coefficients of different sign. A key feature of these models is the…
We consider the conservative complex Swift-Hohenberg equation, which belongs to the family of nonlinear fourth-order dispersive Schr\"odinger equations. In contrast to the well-studied one-dimensional dissipative Swift-Hohenberg equation,…
We study transmission stabilization of optical solitons against emission of radiation in nonlinear optical waveguides in the presence of weak linear gain-loss, cubic loss, and the collisional Raman frequency shift. We first show how the…
Theories of localised pattern formation are important to understand a broad range of natural patterns, but are less well-understood than more established mechanisms of domain-filling pattern formation. Here, we extend recent work on pattern…
We investigate the existence and linear stability of solitons in the nonlinear Schr\"odinger lattices in the strong coupling regime. Focusing and defocusing nonlinearities are considered, giving rise to bright and dark solitons. In this…
This research investigates the formation and stability of localized states, known as quantum droplets and bubbles, in the quadratic-cubic discrete nonlinear Schr\"odinger equation. Near a Maxwell point, these states emerge from two fronts…
This paper presents the observations of temporally evolving stochastic vibration patterns of a coin vibrating motor. Various voltages are applied to the coin vibrating motor, and the resulting vibrations are recorded using an accelerometer.…
We propose a fundamental setup for the realization of spontaneous symmetry breaking (SSB) and spontaneous antisymmetry breaking (SASB) in the framework of the nonlinear Schroedinger equation with the self-attractive and repulsive cubic…
We derive the equations governing the motion of Kerr solitons in pair waveforms. Recent experiments in microresonators have studied a variety of interaction effects in multisoliton waveforms, including collisions and formation of soliton…
Brain imaging data mapping onto human connectome networks enables the investigation of global brain dynamics, where the brain hubs play an essential role in transferring activity between different brain parts. At this scale, the…
We derive and analyze, analytically and numerically, two first-order continuum models to approximate the nonlinear dynamics of granular crystal lattices, focusing specifically on solitary waves, periodic waves, and dispersive shock waves.…
Thouless pumping is a fundamental phenomenon recognized as being widespread across various areas of physics, with optics holding a particularly prominent role. Here, we study this effect for optical solitons in a medium where the refractive…
We report the first experimental observation of breather gases (BGs) in optics, realized in a recirculating fiber loop enabling virtually lossless propagation over $1200$ km. Initiated by a slowly modulated optical background perturbed by…
A model for internal interfacial waves between two layers of fluid in the presence of current and variable bottom is studied in the flat-surface approximation. Fluids are assumed to be incompressible and inviscid. Another assumption is that…
In this paper we focus on a discrete physical model describing granular crystals, whose equations of motion can be described by a system of differential difference equations (DDEs). After revisiting earlier continuum approximations, we…