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The processes in nonequilibrium dissipative media caused by coherent structure formation and lead to the complicated dynamics are of interest for nonlinear physics. Here we consider a model of the flow of interacting electronics patterns.…
Networks of coupled nonlinear oscillators model a broad class of physical, chemical and biological systems. Understanding emergent patterns in such networks is an ongoing effort with profound implications for different fields. In this work,…
We analyze theoretically the effects of electron-electron and electron-phonon interactions in the dynamics of a system of a few electrons that can be trapped to a localized state and detrapped to an extended band state of a small quantum…
We experimentally study a one-dimensional uncompressed granular chain composed of a finite number of identical spherical beads with Hertzian interactions. The chain is harmonically excited by an amplitude- and frequency-dependent boundary…
The propagation of an initially Gaussian wave packet of width $\Delta_0$ in a cubic non-linear Schrodinger equation with a negative coupling constant for the nonlinear term is considered . It is predicted analytically and verified…
In this paper we develop novel results on self triggering control of nonlinear systems, subject to perturbations and actuation delays. First, considering an unperturbed nonlinear system with bounded actuation delays, we provide conditions…
Condensed matter physics at room temperature usually assumes that electrons in conductors can be described as spatially narrow wave packets - in contrast to what the Schr\"odinger equation would predict. How a finite-temperature environment…
Using a discrete mode approach we investigate the intermodal dynamics in a frequency comb with nonlinear coupling due to four-wave mixing. In the presence of sufficient saturable absorption, phase space collapses into a single state, and…
For the hopping dynamics in a one-dimensional model, containing energy and barrier disorder, we determine the linear and nonlinear response to an external field for arbitrary external frequencies. The calculation is performed in analytical…
Pauli paramagnetic susceptibility $\chi$ is unaffected by the electron-phonon interaction in the Migdal-Eliashberg context. Fullerene compounds however do not fulfill the adiabatic assumption of Migdal's theorem and nonadiabatic effects are…
There are three key factors of a system of coupled oscillators that characterize the interaction among them: coupling (how to affect), delay (when to affect) and topology (whom to affect). For each of them, the existing work has mainly…
The dynamical screening of the electron--phonon vertex is caused by the retarded oscillations of the electronic charge following the electron--hole scattering with a phonon mode. This retardation induces a frequency dependence of the…
We present trapped solitary wave solutions of a coupled nonlinear Schr\"odinger system in $1$+$1$ dimensions in the presence of an external, supersymmetric and complex $\mathcal{PT}$-symmetric potential. The Schr\"odinger system this work…
We study the dynamics of solitary waves traveling in a one-dimensional chain of bistable elements in the presence of a local inhomogeneity (defect). Numerical simulations reveal that depending upon its initial speed, an incoming solitary…
We investigate the effect of a current nonlinearity on the evolution of a trapped atomic Bose-Einstein condensate. We have implemented techniques from the field of nonlinear optics to provide new insights into the irregular dynamics…
We develop a theory to address the non-equilibrium dynamics of phonons in a one-dimensional trapped ion system. We elaborate our earlier results obtained in Phys. Rev. Lett. {\bf 111}, 170406 (2013) to chart out the mechanism of…
In this article, we study wave dynamics in the fractional nonlinear Schr\"odinger equation with a modulated honeycomb potential. This problem arises from recent research interests in the interplay between topological materials and nonlocal…
This paper presents an improved version of the previously proposed self-consistent drift-diffusion-reaction model correcting for non-physical behavior at longer time scales. To this end a novel boundary condition is employed that takes into…
One-dimensional nonlinear phononic crystals have been assembled from periodic diatomic chains of stainless steel cylinders alternated with Polytetrafluoroethylene (PTFE) spheres. We report the presence of acoustic band gaps in the…
Impedance matching is one of the most important practice in wave engineering as it enables to maximize the power transfer from the signal source to the load in the wave system. Unfortunately, it is bounded by the Bode-Fano criterion that…