Impulse-induced localized nonlinear modes in an electrical lattice

Intrinsic localized modes, also called discrete breathers, can exist under certain conditions in one-dimensional nonlinear electrical lattices driven by external harmonic excitations. In this work, we have studied experimentally the efectiveness of generic periodic excitations of variable waveform at generating discrete breathers in such lattices. We have found that this generation phenomenon is optimally controlled by the impulse transmitted by the external excitation (time integral over two consecutive zerosComment: 5 pages, 8 figure

Speed-of-light pulses in a nonlinear Weyl equation

We introduce a prototypical nonlinear Weyl equation, motivated by recent developments in massless Dirac fermions, topological semimetals and photonics. We study the dynamics of its pulse solutions and find that a localized one-hump initial condition splits into a localized two-hump pulse, while an associated phase structure emerges in suitable components of the spinor field. For times larger than a transient time $t_s$ this pulse moves with the speed of light (or Fermi velocity in Weyl semimetals), effectively featuring linear wave dynamics and maintaining its shape (both in two and three dimensions). We show that for the considered nonlinearity, this pulse represents an exact solution of the nonlinear Weyl (NLW) equation. Finally, we comment on the generalization of the results to a broader class of nonlinearities and on their emerging potential for observation in different areas of application.Comment: 7 pages, 6 figure

Effect of breather existence on reconstructive transformations in mica muscovite

The International Workshop on Complex Systems (5º. 2007. Sendai, Japan)Reconstructive transformations of layered silicates as mica muscovite take place at much lower temperatures than expected. A possible explanation is the existence of breathers within the potassium layer. Numerical analysis of a model shows the existence of many different types of breathers with different energies and existence ranges which spectrum coincides approximately with a statistical theory for them.Ministerio de Educacion y Ciencia, Spain, project FIS2004-0118

Moving discrete breathers in a Klein–Gordon chain with an impurity

We analyse the influence of an impurity in the evolution of moving discrete breathers in a Klein–Gordon chain with non-weak nonlinearity. Three different types of behaviour can be observed when moving breathers interact with the impurity: they pass through the impurity continuing their direction of movement; they are reflected by the impurity; they are trapped by the impurity, giving rise to chaotic breathers, as their Fourier power spectra show. Resonance with a breather centred at the impurity site is conjectured to be a necessary condition for the appearance of the trapping phenomenon. This paper establishes a difference between the resonance condition of the non-weak nonlinearity approach and the resonance condition with the linear impurity mode in the case of weak nonlinearity.European Commission under the RTN project LOCNET, HPRN-CT-1999-0016

Moving breathers in a DNA model with competing short and long range dispersive interactions

Moving breathers is a means of transmitting information in DNA. We study the existence and properties of moving breathers in a DNA model with short range interaction, due to the stacking of the base pairs, and long range interaction, due to the finite dipole moment of the bond within each base pair. In our study, we have found that mobile breathers exist for a wide range of the parameter values, and the mobility of these breathers is hindered by the long range interaction. This fact is manifested by: (a) an increase of the effective mass of the breather with the dipole–dipole coupling parameter; (b) a poor quality of the movement when the dipole–dipole interaction increases; and (c) the existence of a threshold value of the dipole–dipole coupling above which the breather is not movable. An analytical formula for the boundaries of the regions where breathers are movable is calculated. Concretely, for each value of the breather frequency, it can be obtained the maximum value of the dipole–dipole coupling parameter and the maximum and minimum values of the stacking coupling parameter where breathers are movable. Numerical simulations show that, although the necessary conditions for the mobility are fulfilled, breathers are not always movable. Finally, the value of the dipole–dipole coupling constant is obtained through quantum chemical calculations. They show that the value of the coupling constant is small enough to allow a good mobility of breathers.European Commission under the RTN project LOCNET, HPRN-CT-1999-0016

Discrete Breathers in Klein-Gordon Lattices: a Deflation-Based Approach

Deflation is an efficient numerical technique for identifying new branches of steady state solutions to nonlinear partial differential equations. Here, we demonstrate how to extend deflation to discover new periodic orbits in nonlinear dynamical lattices. We employ our extension to identify discrete breathers, which are generic exponentially localized, time-periodic solutions of such lattices. We compare different approaches to using deflation for periodic orbits, including ones based on a Fourier decomposition of the solution, as well as ones based on the solution's energy density profile. We demonstrate the ability of the method to obtain a wide variety of multibreather solutions without prior knowledge about their spatial profile

Moving breathers in bent DNA with realistic parameters

Recent papers have considered moving breathers (MBs) in DNA models including long range interaction due to the dipole moments of the hydrogen bonds. We have recalculated the value of the charge transfer when hydrogen bonds stretch using quant um chemical methods which takes into account the whole nucleoside pairs. We explore the conseque nces of this value on the properties of MBs, including the range of frequencies for which they exi st and their effective masses. They are able to travel through bending points with fairly large c urvatures provided that their kinetic energy is larger than a minimum energy which depends on the cu rvature. These energies and the corresponding velocities are also calculated in function o f the curvatureMECD–FEDER project BMF2003- 03015/FIS

Numerical study of two-dimensional disordered Klein-Gordon lattices with cubic soft anharmonicity

Localized oscillations appear both in ordered nonlinear lattices (breathers) and in disordered linear lattices (Anderson modes). Numerical studies on a class of two-dimensional systems of the Klein-Gordon type show that there exist two different types of bifurcation in the path from nonlinearity-order to linearity-disorder: inverse pitchforks, with or without period doubling, and saddle-nodes. This was discovered for a one-dimensional system in a previous work of Archilla, MacKay and Marin. The appearance of a saddle-node bifurcation indicates that nonlinearity and disorder begin to interfere destructively and localization is not possible. In contrast, the appearance of a pitchfork bifurcation indicates that localization persists

Discrete breathers collisions in nonlinear Schrödinger and Klein-Gordon lattices

Collisions between moving localized modes (moving breathers) in non- integrable lattices present a rich outcome. In this paper, some features of the interaction of moving breathers in Discrete Nonlinear Schrödinger and Klein- Gordon lattices, together with some plausible explanations, are exposed