Pattern Formation and Solitons
Nonlinear waveguides with two distinct domains of anomalous dispersion can support the formation of molecule-like two-color pulse compounds. They consist of two tightly bound subpulses with frequency loci separated by a vast frequency gap.…
We put forth two physics-informed neural network (PINN) schemes based on Miura transformations and the novelty of this research is the incorporation of Miura transformation constraints into neural networks to solve nonlinear PDEs. The most…
We numerically investigate the long time dynamics of spatially periodic breather solutions of the 1-D nonlinear Schr\"odinger equation under parametric forcing of the form $f(x)=f_0 \exp(iKx)$ along with dissipation. In the absence of…
We establish stability and characteristics of two-dimensional (2D) vortex ring-shaped quantum droplets (QDs) formed by binary Bose-Einstein condensates (BECs). The system is modeled by the Gross-Pitaevskii (GP) equation with the cubic term…
Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and…
Synchronous collisions of solitons of the Korteweg -- de Vries equation are considered as a representative example of the interaction of a large number of solitons in a soliton gas. Statistical properties of the soliton field are examined…
We consider Hodgkin-Huxley-type model that is a stiff ODE system with two fast and one slow variables. For the parameter ranges under consideration the original version of the model has unstable fixed point and the oscillating attractor…
An activator-inhibitor-substrate model of side-branching used in the context of pulmonary vascular and lung development is considered on the supposition that spatially localized concentrations of the activator trigger local side-branching.…
We investigate the nonequilibrium dynamics of two-dimensional Bose-Einstein condensates in boxlike traps with power-law potential boundaries by quenching the interatomic interactions. For both concave and convex potentials, we show that…
We show that a number of nonlocal nonlinear equations including the Ablowitz-Musslimani and the Yang variant of the nonlocal nonlinear Schr\"od-inger (NLS) equation, nonlocal modified Korteweg de Vries (mKdV) equation as well as the…
Reaction-diffusion waves in multiple spatial dimensions advance at a rate that strongly depends on the curvature of the wave fronts. These waves have important applications in many physical, ecological, and biological systems. In this work,…
Intermode interactions in one-dimensional nonlinear periodic structures have been studied by many authors, starting with the classic work by Fermi, Pasta, and Ulam (FPU) in the middle of the last century. However, symmetry selection rules…
We study the phenomenon of synchronization in pairs of doubly clamped, mechanically coupled silicon micro-oscillators. A continuous-wave laser beam is used to drive the micro-beams into limit cycle oscillations and to detect the…
In recent years, there has been considerable interest in the study of wave propagation in nonlinear photonic lattices. The interplay between nonlinearity and periodicity has led researchers to manipulate light and discover new and…
We study acoustic-gravity waves in a quasi-isothermal atmosphere in the presence of a weak random addition to the vertical temperature profile, which simulates the real atmosphere of the Earth at altitudes greater than $\sim 200$ km. The…
Data-driven forward-inverse problems for the variable coefficients Hirota (VCH) equation are discussed in this paper. The main idea is to use the improved physics-informed neural networks (IPINN) algorithm with neuron-wise locally adaptive…
We examine analytically and numerically the effect of fractionality on a saturable bulk and surface impurity embedded in a 1D lattice. We use a fractional Laplacian introduced previously by us, and by the use of lattice Green functions we…
Many-body long-range interacting systems can remain approximately in a quasi-stationary state far-from-thermodynamic equilibrium. These states are typically characterized by a pair of counter-propagating density clusters, or by a single…
We study the formation of lines in phase space in Wigner's distribution $W.$ Whereas lines in phase space do not form in classical systems, unless special initial states are chosen, we find, for large classes of systems and initial states…
We systematically investigate rogue wave's spatial-temporal pattern in $N$ $(N\geq2)$-component coupled defocusing nonlinear Schr\"{o}dinger equations. The fundamental rogue wave solutions are given in a unified form for both focusing and…