Related papers: Anomalous correlators, "ghost" waves and nonlinear…
In weakly nonlinear dispersive wave systems, long-time dynamics are typically governed by time resonances, where wave phases evolve coherently due to exact frequency matching. Recent advances in spatio-temporal spectrum measurements,…
The time-asymptotic behavior of undamped, nonlinear oscillators with a random frequency is investigated analytically and numerically. We find that averaged quantities of physical interest, such as the oscillator's mechanical energy,…
This article is concerned with the rigorous validation of anomalous spreading speeds in a system of coupled Fisher-KPP equations of cooperative type. Anomalous spreading refers to a scenario wherein the coupling of two equations leads to…
Understanding the interplay between different wave excitations, such as phonons and localized solitons, is crucial for developing coarse-grained descriptions of many-body, near-integrable systems. We treat the Fermi-Pasta-Ulam-Tsingou…
The description of shock waves beyond the shock point is a challenge in nonlinear physics. Finding solutions to the global dynamics of dispersive shock waves is not always possible due to the lack of integrability. Here we propose a new…
Recent advances in non-Hermitian physical systems have led to numerous novel optical phenomena and applications. However, most realizations are limited to classical systems and quantum fluctuations of light is unexplored. For the first…
In this letter we consider the phase diffusion of a harmonically driven undamped pendulum and show that it is anomalous in the strong sense. The role played by the fractal properties of the phase space is highlighted, providing an…
We study various temporal correlation functions of a tagged particle in one-dimensional systems of interacting point particles evolving with Hamiltonian dynamics. Initial conditions of the particles are chosen from the canonical thermal…
Chimera states are firstly discovered in nonlocally coupled oscillator systems. Such a nonlocal coupling arises typically as oscillators are coupled via an external environment whose characteristic time scale $\tau$ is so small (i.e., $\tau…
Anomalous diffusion often arises in complex environments where viscoelastic or crowded conditions influence particle motion. In many biological and soft-matter systems, distinct components of the medium exhibit unique viscoelastic…
We present a detailed analysis of the modulational instability of the zone-boundary mode for one and higher-dimensional Fermi--Pasta--Ulam (FPU) lattices. The growth of the instability is followed by a process of relaxation to…
Motivated by recent experiments [Lin {\it et al.}, Nature {\bf 417}, 83 (2011)] that engineered spin-orbit coupling in ultra-cold mixtures of bosonic atoms, we study the dipole oscillation of trapped spin-orbit-coupled non-condensed Bose…
The foundations of weak turbulence theory is explored through its application to the (alpha) Fermi-Pasta-Ulam (FPU) model, a simple weakly nonlinear dispersive system. A direct application of the standard kinetic equations would miss…
In the present paper we consider dispersion curves of longitudinal excitations of a model core-softened liquid and SPC/E model of water. We show that both systems demonstrate anomalous behavior of the excitation frequencies: the frequencies…
The computational investigation of Fermi, Pasta, Ulam, and Tsingou of arrays of nonlinearly coupled oscillators has led to a wealth of studies in nonlinear dynamics. Most studies of oscillator arrays have considered homogeneous oscillators,…
We analyze a class of linear shell models subject to stochastic forcing in finitely many degrees of freedom. The unforced systems considered formally conserve energy. Despite being formally conservative, we show that these dynamical systems…
We investigate a possibility of realization of structurally stable chaotic dynamics in neural systems. The considered model of interacting neurons consists of a pair of coupled FitzHugh-Nagumo systems, with the parameters being periodically…
Nonlinear normal modes are periodic orbits that survive in nonlinear chains, whose instability plays a crucial role in the dynamics of many-body Hamiltonian systems toward thermalization. Here we focus on how the stability of nonlinear…
Continuum elasticity is a powerful tool applicable in a broad range of physical systems and phenomena. Yet, understanding how and on what scales material disorder may lead to the breakdown of continuum elasticity is not fully understood. We…
Commonly, thermal transport properties of one-dimensional systems are found to be anomalous. Here, we perform a numerical and theoretical study of the $\beta$-FPUT chain, considered a prototypical model for one-dimensional anharmonic…