Pattern Formation and Solitons
We study the dynamics of a Josephson junction connected to a dc current supply via a distributed parameter capacitor, which serves as a resonator. We reveal multistability in the current-voltage characteristic of the system; this…
A spiral wave is a macroscopic dynamic of excitable media that plays an important role in several distinct systems, including the Belousov-Zhabotinsky reaction, seizures in the brain, and lethal arrhythmia in the heart. Because spiral wave…
In this work we study the dynamical behavior of two interacting vortex pairs, each one of them consisting of two point vortices with opposite circulation in the 2d plane. The vortices are considered as effective particles and their…
In our recent study the maximal values of kinetic and potential energy densities that can be achieved in the collisions of $N$ slow kinks in the sine-Gordon model were calculated analytically (for $N=1,2$, and 3) and numerically (for $4\le…
With the recent exponential growth of applications using artificial intelligence (AI), the development of efficient and ultrafast brain-like (neuromorphic) systems is crucial for future information and communication technologies. While the…
Superregular (SR) breathers are nonlinear wave structures formed by a unique nonlinear superposition of pairs of quasi-Akhmediev breathers. They describe a complete scenario of modulation instability that develops from localized small…
The subject of PT-symmetry and its areas of application have been blossoming over the past decade. Here, we consider a nonlinear Schr\"odinger model with a complex potential that can be tuned controllably away from being PT-symmetric, as it…
Rogue waves are extreme and rare fluctuations of the wave field that have been discussed in many physical systems. Their presence substantially influences the statistical properties of an incoherent wave field. Their understanding is…
We present the full classification of wave patterns evolving from an initial step-like discontinuity for arbitrary choice of boundary conditions at the discontinuity location in the DNLS equation theory. In this non-convex dispersive…
We consider the Riemann problem of evolution of initial discontinuities for the photon fluid propagating in a normal dispersion fiber with account of self-steepening effects. The dynamics of light field is described by the nonlinear…
Neural field equations model population dynamics of large-scale networks of neurons. Wave propagation in neural fields is often studied by constructing traveling wave solutions in the wave coordinate frame. Nonequilibrium dynamics are more…
The defining property of chimera states is the coexistence of coherent and incoherent domains in systems that are structurally and spatially homogeneous. The recent realization that such states might be common in oscillator networks raises…
We report on the experimental study of an optically driven multimode semiconductor laser with 1~m cavity length. We observed a spatiotemporal regime where real time measurements reveal very high intensity peaks in the laser field. Such a…
We introduce a one-dimensional model based on the nonlinear Schrodinger/Gross-Pitaevskii equation where the local nonlinearity is subject to spatially periodic modulation in terms of the Jacobi dn function, with three free parameters…
In this work, we study the wave propagation in a recently proposed acoustic structure, the locally resonant granular crystal. This structure is composed of a one-dimensional granular crystal of hollow spherical particles in contact,…
Since its discovery in 2002, the chimera state has frequently been described as a counter-intuitive, puzzling phenomenon. The Kuramoto model, in contrast, has become a celebrated paradigm useful for understanding a range of phenomena…
We study the dynamics and interaction of coaxial vortex rings in the FitzHugh-Nagumo excitable medium. We find that threading vortex rings with a vortex string results in significant qualitative differences in their evolution and…
We consider the discrete Swift-Hohenberg equation with cubic and quintic nonlinearity, obtained from discretizing the spatial derivatives of the Swift-Hohenberg equation using central finite differences. We investigate the discretization…
We present an experimental system of networks of coupled non-linear chemical reactors, which we theoretically model within a reaction-diffusion framework. The networks consist of patterned arrays of diffusively coupled nanoliter-scale…
Rotating scroll waves are self-organising patterns which are found in many oscillating or excitable systems. Here we show that quasi-periodic (meandering) scroll waves, which include the rotors that organise cardiac arrhythmias, exhibit…