Related papers: Wave localization in strongly nonlinear Hertzian c…

Nonlinear gyrotropic medium is a medium, whose natural optical activity depends on the intensity of the incident light wave. The Kuhn's model is used to study nonlinear gyrotropic medium with great success. The Kuhn's model presents itself…

We examine the long-term behaviour of non-integrable, energy-conserved, 1D systems of macroscopic grains interacting via a contact-only generalized Hertz potential and held between stationary walls. Existing dynamical studies showed the…

We present a new description of nonequilibrium square patterns as a harmonically coupled crystal lattice. In a vertically oscillating granular layer, different transverse normal modes of the granular square-lattice pattern are observed for…

We study quasiperiodicity-induced localization of waves in strongly precompressed granular chains. We propose three different setups, inspired by the Aubry--Andr\'e (AA) model, of quasiperiodic chains; and we use these models to compare the…

In this paper, the effect of weak nonlinearities in 1D locally resonant metamaterials is investigated via the method of multiple scales. Commonly employed to the investigate the effect of weakly nonlinear interactions on the free wave…

We uncover the interaction-induced \emph{stable self-localization} of bosons in disorder-free superlattices. In these nonthermalized multi-particle states, one of the particles forms a superposition of multiple standing waves, so that it…

This work investigates the weakly nonlinear dynamics of internal shear layers and the mean zonal flow induced by the longitudinal libration of an inner core within a spherical shell. Building on the work of He et al. (J. Fluid Mech., vol.…

We consider a system of coupled nonlinear Schr{\"o}dinger equations in one space dimension. First, we prove the existence of multi-speed solitary waves, i.e solutions to the system with each component behaving at large times as a solitary…

A high-frequency asymptotic scheme is generated that captures the motion of waves within discrete hexagonal and honeycomb lattices by creating continuum homogenised equations. The accuracy of these effective medium equations in describing…

We derive and justify analytically the dynamics of a small macroscopically modulated amplitude of a single plane wave in a nonlinear diatomic chain with stabilizing on-site potentials including the case where a wave generates another wave…

Thanks to their immense purity and controllability, dipolar Bose-Einstein condensates are an exemplar for studying fundamental non-local nonlinear physics. Here we show that a family of fundamental nonlinear waves - the dark solitons - are…

A theoretical analysis about the influence of the Hertz elastic contact on a three body chain collision is presented. In spite of the elastic character of the collision, the final velocity of each particle depends on the particular…

We introduce a nonlinear photonic system that enables asymmetric localization and unidirectional transfer of an electromagnetic wave through the second harmonic generation process. Our proposed scattering setup consists of a…

The focus of our work is dispersive, second-order effective model describing the low-frequency wave motion in heterogeneous (e.g.~functionally-graded) media endowed with periodic microstructure. For this class of quasi-periodic medium…

We consider the nonlinear Dirac equations (NLDE's) in 1+1 dimension with scalar-scalar self interaction $\frac{g^2}{\kappa+1} ({\bPsi} \Psi)^{\kappa+1}$ in the presence of various external electromagnetic fields. Starting from the exact…

Nonlinearities can have a profound influence on the dynamics and equilibrium properties of discrete lattice systems. The simple case of two coupled modes with self-nonlinearities gives rise to the rich bosonic Josephson effects. In…

In this paper, modulation instability and nonlinear supratransmission are investigated in a one-dimensional chain of atoms using cubic-quartic nonlinearity coefficients. As a result, we establish the discrete nonlinear evolution equation by…

In the absence of nonlinearity all normal modes (NMs) of a chain with disorder are spatially localized (Anderson localization). We study the action of nonlinearity, whose strength is ramped linearly in time. It leads to a spreading of a…

In two dimensional disordered lattices, presence of interaction makes particles less localized than the non-interacting ones within the range of disorder strength $W \le 4$ and interaction strength $V \le 4$. If the interaction strength is…

We theoretically study the electric pulse-driven non-linear response of interacting bosons loaded in an optical lattice in the presence of an incommensurate superlattice potential. In the non-interacting limit $(U=0)$, the model admits both…