Metapopulation models have been a popular tool for the study of epidemic spread over a network of highly populated nodes ...

The discrete complex Ginzburg–Landau equation is a fundamental model for the dynamics of nonlinear lattices incorporating ...

We consider a previously experimentally realized discrete model that describes a mechanical metamaterial consisting of a ...

It is widely accepted that the number of reported cases during the first stages of the COVID-19 pandemic severely ...

We consider the existence and spectral stability of multi-breather structures in the discrete Klein–Gordon equation, both ...

In this work we revisit the existence, stability and dynamical properties of moving discrete breathers in -FPU lattices. ...

In the present work we provide a characterization of the ground states of a higher-dimensional quadratic-quartic model of ...

The Ablowitz–Ladik system, being one of the few integrable nonlinear lattices, admits a wide class of analytical solutions, ...

While the Ablowitz-Ladik lattice is integrable, the Discrete Nonlinear Schrödinger equation, which is more significant for ...

In the present work, we revisit a recently proposed and experimentally realized topological two-dimensional lattice with ...

For a one-dimensional linear lattice, earlier work has shown how to systematically construct a slowly- decaying linear ...

We examine the spatial modeling of the outbreak of COVID-19 in two regions: the autonomous community of Andalusia in Spain ...

We revisit the problem of transverse instability of a 2D breather stripe of the sine-Gordon (sG) equation. A numerically ...

Guided by a rigorous mathematical result, we have earlier introduced a numerical algorithm, which using as input the ...

Following the highly restrictive measures adopted by many countries for combating the current pandemic, the number of ...

Following the highly restrictive measures adopted by many countries for combating the current pandemic, the number of ...

We examine - both experimentally and numerically - a two-dimensional nonlinear driven electrical lattice with honeycomb ...

The role of lockdown measures in mitigating COVID-19 in Mexico is investigated using a comprehensive nonlinear ODE model. ...

The Salerno model is a discrete variant of the celebrated nonlinear Schr¨odinger (NLS) equation interpolating between the ...

We examine - both experimentally and numerically - a two-dimensional nonlinear driven electrical lattice with honeycomb ...

In this work we revisit a classical problem of traveling waves in a damped Frenkel–Kontorova lattice driven by a constant ...

The aim of the present work is to examine the role of discreteness in the interaction of both co-winding and counter-winding ...

The interplay of nonlinearity and topology results in many novel and emergent properties across a number of physical systems ...

The influence of one dimensional substrate patterns on the nanocolumnar growth of thin films deposited by magnetron ...

In this work, we explore a massless nonlinear Dirac equation, i.e., a nonlinear Weyl equation. We study the dynamics of ...

We introduce a generalized version of the Ablowitz-Ladik model with a power-law nonlinearity, as a discretization of the ...

We observe dark and bright intrinsic localized modes (ILMs), also known as discrete breathers, experimentally and numerically ...

Intrinsic localized modes, also called discrete breathers (DBs), can exist under certain conditions in one-dimensional ...

In this Chapter, we touch upon the wide topic of discrete breather (DB) formation with a special emphasis on the prototypical ...

The existence of stationary solitary waves in symmetric and non-symmetric complex potentials is studied by means of ...

We demonstrate a possibility to make rogue waves (RWs) in the form of the Peregrine soliton (PS) and Kuznetsov-Ma breathers ...

In this work, we numerically consider the initial value problem for nonlinear Schrodinger (NLS)-type models arising in ...

The subject of PT -symmetry and its areas of application have been blossoming over the past decade. Here, we consider a ...

In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. ...

Quantum vortices, the quantized version of classical vortices, play a prominent role in superfluid and superconductor phase ...

We study a two-dimensional incoherently pumped exciton-polariton condensate described by an open-dissipative Gross-Pitaevskii ...

In this manuscript we review the possibility of inducing large coherence in a macroscopic dense target by using adiabatic ...

We study the dynamics of dark solitons in an incoherently pumped exciton-polariton condensate by means of a system composed ...

In the present work, we aim at taking a step towards the spectral stability analysis of Peregrine solitons, i.e., wave ...

In this work, we revisit a criterion, originally proposed in [Nonlinearity 17, 207 (2004)], for the stability of solitary ...

In the present work, we explore a nonlinear Dirac equation motivated as the continuum limit of a binary waveguide array ...

In this work, we provide two complementary perspectives for the (spectral) stability of solitary traveling waves in ...

In the present work, we explore the possibility of excited breather states in a nonlinear Klein–Gordon lattice to become ...

In the present work, we consider a prototypical example of a PT -symmetric Dirac model. We discuss the underlying linear ...

Discrete breathers are ubiquitous structures in nonlinear anharmonic models ranging from the prototypical example of the ...

In this work, we employ the SO(2)-rotations of a two-component, one-, two- and three-dimensional nonlinear Schr¨odinger ...

Locally decreasing the impulse transmitted by periodic pulses is shown to be a reliable method of taming chaos in starlike ...

We explore a prototypical two-dimensional massive model of the nonlinear Dirac type and examine its solitary wave and ...

As an extension of the class of nonlinear PT-symmetric models, we propose a system of sine-Gordon equations, with the PT ...

We study discrete breathers in prototypical nonlinear oscillator networks subjected to nonharmonic zero-mean periodic ...

In the present work, we combine the notion of parity-time (PT ) symmetry with that of supersymmetry (SUSY) for a prototypical ...

In the present work, we explore the case of a general PT -symmetric dimer in the context of two both linearly and nonlinearly ...

In the present work, we introduce a discrete formulation of the nonlinear Dirac equation in the form of a discretization ...

In the present Chapter, we consider two prototypical Klein-Gordon models: the integrable sine- Gordon equation and the ...

We consider the existence, stability and dynamics of the nodeless state and fundamental nonlinear excitations, such as ...

In this work, we explore a prototypical example of a genuine continuum breather (i.e., not a standing wave) and the ...

There exist in nature examples of lattices of elements for which the interaction is repulsive, the elements are kept in ...

A collective coordinate theory is developed for soliton ratchets in the damped discrete sine-Gordon model driven by a ...

We study the effects of management of the PT-symmetric part of the potential within the setting of Schrödinger dimer and ...

We study deterministic escape dynamics of the discrete Klein-Gordon model with a repulsive quartic on-site potential. Using ...

Intrinsic localized modes (ILMs) have been generated and characterized in two-dimensional nonlinear electrical ...

We study the coupling between backward- and forward-propagating wave modes, with the same group velocity, in a composite ...

We discuss the existence of breathers and lower bounds on their power, in nonlinear Schrödinger lattices with nonlinear ...

We study the existence and stability of multibreathers in Klein-Gordon chains with interactions that are not restricted ...

We report the observation of spontaneous localization of energy in two spatial dimensions in the context of nonlinear ...

We provide a systematic analysis of a prototypical nonlinear oscillator system respecting PT symmetry i.e., one of them ...

In this work, we examine the collision of an atomic dark-bright soliton, in a two-component Bose-Einstein condensate, with ...

We prove nonexistence of breathers (spatially localized and time-periodic oscillations) for a class of Fermi-Pasta-Ulam ...

The interaction of matter-wave solitons with a potential barrier is a fundamentally important problem, and the splitting ...

In the present work, we examine “binary” waveguide arrays, where the coupling between adjacent sites alternates between ...

We study the existence, stability, and dynamics of symmetric and anti-symmetric states of quasi-one-dimensional polariton ...

Motivated by recent experimental results, we study beating dark-dark solitons as a prototypical coherent structure that ...

We show experimentally and numerically that an intrinsic localized mode (ILM) can be stably produced (and experimentally ...

We study localized waves in chains of oscillators coupled by Hertzian interactions and trapped in local potentials. This ...

the present work, we numerically explore the existence and stability properties of different types of configurations of ...

We study the propagation of quasidiscrete microwave solitons in a nonlinear left-handed coplanar waveguide coupled with ...

We develop a simple 1D model for the scattering of an incoming particle hitting the surface of mica crystal, the transmission ...

In the present work, we consider the dynamics of dark solitons as one mode of a defocusing photorefractive lattice coupled ...

Non-time reversible phonobreathers are non-linear waves that can transport energy in coupled oscillator chains by means ...

We study experimentally and numerically the existence and stability properties of discrete breathers in a periodic nonlinear ...

In this paper, we give a proof of the existence of stationary dark solitonsolutions or heteroclinic orbits of nonlinear ...

In this paper, interstitial migration generated by scattering with a mobile breather is investigated numerically in a ...

We study the dynamics of matter waves in an effectively one-dimensional Bose-Einstein condensate in a double-well potential. ...

In this work, we revisit the question of stability of multibreather configurations, i.e. discrete breathers with multiple ...

We study the existence, stability, and dynamics of the ground state and nonlinear excitations, in the form of dark solitons, ...

We discuss the existence of breathers and of energy thresholds for their formation in DNLS lattices with linear and nonlinear ...

Ratchet dynamics of topological solitons of the forced and damped discrete double sine-Gordon system are studied. Directed ...

We study the discrete nonlinear Schrödinger lattice model with the onsite nonlinearity of the general form, |u|2σu|u|2σu. ...

In this paper, we construct, by means of similarity transformations, explicit solutions to the cubic–quintic nonlinear ...

In this work, we present a mechanical example of an experimental realization of a stability reversal between on-site and ...

By applying a staggered driving force in a prototypical discrete model with a quartic nonlinearity, we demonstrate the ...

We investigate the collisions of moving breathers, with the same frequency, in three different Klein-Gordon chains of ...

We consider the existence, stability and dynamical evolution of dark vortex states in the two-dimensional defocusing DNLS ...

We propose analytical lower and upper estimates on the excitation threshold for breathers (in the form of spatially localized ...

We consider collisions of moving breathers (MBs) in the Peyrard-Bishop DNA model. Two identical stationary breathers, ...

We consider an infinite chain of particles linearly coupled to their nearest neighbors and subject to an anharmonic local ...

We study families of one-dimensional matter-wave bright solitons supported by the competition of contact and dipole-dipole ...

In this paper, we consider the existence, stability and dynamical evolution of dark vortex states in the two-dimensional ...

The past few years have witnessed an explosion of interest in discrete models and intrinsic localized modes (discrete ...

In the present work, we propose a new set of coherent structures that arise in nonlinear dynamical lattices with more than ...

The present work examines in detail the existence, stability and dynamics of travelling solitary waves in a Schrödinger ...

We study four diferent approximations for finding the profile of discrete solitons in the one-dimensional Discrete Nonlinear ...

Reconstructive transformations of layered silicates as mica muscovite take place at much lower temperatures than expected. ...

Collisions between moving localized modes (moving breathers) in non- integrable lattices present a rich outcome. In this ...

We study the collisions of moving breathers with the same frequency, traveling with opposite directions within a Klein–Gordon ...

We consider the question of existence of periodic solutions (called breather solutions or discrete solitons) for the ...

In this paper we analyze the existence, stability, dynamical formation, and mobility properties of localized solutions in ...

We introduce a two-dimensional discrete nonlinear Schrödinger (DNLS) equation with self-attractive cubic nonlinearity in ...

Interstitials and vacancies, in one-dimensional lattices, are point defects that can be modelled by means of kinks or ...

The quantum state diffusion equation is applied to the problem of energy transfer in proteins. Lindblad operators, capable ...

The long-standing problem of moving discrete solitary waves in nonlinear Schrödinger lattices is revisited. The context ...

We consider polarons in models of coupled electronic and vibrational degrees of freedom, in the presence of a soft nonlinear ...

We study the dynamics of moving discrete breathers in an interfaced piecewise DNA molecule. This is a chain in which all ...

Reconstructive transformations in layered silicates need a high temperature in order to be observed. However, very recently, ...

We study the symmetric collisions of two mobile breathers/solitons in a model for coupled wave guides with a saturable ...

In this paper a Frenkel–Kontorova model with a nonlinear int eraction potential is used to describe a vacancy defect in a ...

In this poster we show some recent results concerning discrete solitons in strong optical lattices, which can be described ...

We demonstrate the possibility for explicit construction in a discrete Hamiltonian model of an exact solution of the form ...

Discrete breathers, or intrinsic localized modes, are spatially localized, time–periodic, nonlinear excitations that can ...

We present some results on breather collisions in DNLS lattices, with special focus on systems with saturable nonlinearity. ...

Using a theorem dubbed the multibreather stability theorem (Archilla J F R et al 2003 Physica D 180 235) we have obtained ...

We demonstrate that time-periodic modulation of the nonlinearity coefficient in the discrete nonlinear Schrödinger equation ...

Recent papers have considered moving breathers (MBs) in DNA models including long range interaction due to the dipole ...

In this paper we study the existence and linear stability of bright and dark breathers in one-dimensional FPU lattices. ...

In this paper, we examine a nonlinear model with an impurity emulating a bend. We justify the geometric interpretation of ...

A vacancy defect is described by a Frenkel-Kontorova model with a discommensuration. This vacancy can migrate when interacts ...

Whereas there exists a mathematical proof for one-site breathers stability, and an unpublished one for two-site breathers, ...

We analyze the influence of an impurity in the evolution of moving discrete breathers in a Klein–Gordon chain with non-weak ...

We study the properties of moving breathers in a bent DNA model with short range interaction, due to the stacking of ...

The existence, stability and movability of breathers in a model for alpha-helix proteins is studied. This model basically ...

There are two different sources of localization in discrete lattices: • Anderson modes in disordered harmonic lattices [1] • Discrete breathers in homogeneous nonlinear lattices [2]

We analyse the influence of an impurity in the evolution of moving discrete breathers in a Klein–Gordon chain with non-weak ...

Moving breathers is a means of transmitting information in DNA. We study the existence and properties of moving breathers ...

So far, all the studies on breathers on DNA have considered models with either short–range or long-range interaction. ...

Localized oscillations appear both in ordered nonlinear lattices (breathers) and in disordered linear lattices (Anderson ...