Dissipative lattice model with exact traveling discrete kink-soliton solutions: Discrete breather generation and reaction diffusion regime

Laboratoire d'Electronique, Informatique et Image (LE21) Université de Bourgogne, Aile des Sciences de l'Ingénieur, BP 47870, 21078 Dijon Cedex, France.
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics (Impact Factor: 2.81). 01/2000; 60(6 Pt B):7484-9. DOI: 10.1103/PhysRevE.60.7484
Source: PubMed


We introduce a nonlinear Klein-Gordon lattice model with specific double-well on-site potential, additional constant external force and dissipation terms, which admits exact discrete kink or traveling wave fronts solutions. In the non-dissipative or conservative regime, our numerical simulations show that narrow kinks can propagate freely, and reveal that static or moving discrete breathers, with a finite but long lifetime, can emerge from kink-antikink collisions. In the general dissipative regime, the lifetime of these breathers depends on the importance of the dissipative effects. In the overdamped or diffusive regime, the general equation of motion reduces to a discrete reaction diffusion equation; our simulations show that, for a given potential shape, discrete wave fronts can travel without experiencing any propagation failure but their collisions are inelastic.

Download full-text


Available from: Patrick Marquié, Nov 24, 2014
  • Source
    • "Tanh -function and the Riccati equation are already applied to many lattices described by differential -difference equations . Tanh-function was used for an example for obtaining exact traveling wave solutions of a nonlinear lattice Klein -Gordon model [77]. Tanh-function was used also for obtaining of exact traveling-wave solution of differential -difference equation in [78] . "
    [Show abstract] [Hide abstract]
    ABSTRACT: The method of simplest equation is applied for analysis of a class of lattices described by differential-difference equations that admit traveling-wave solutions constructed on the basis of the solution of the Riccati equation. We denote such lattices as Riccati lattices. We search for Riccati lattices within two classes of lattices: generalized Lotka - Volterra lattices and generalized Holling lattices. We show that from the class of generalized Lotka - Volterra lattices only the Wadati lattice belongs to the class of Riccati lattices. Opposite to this many lattices from the Holling class are Riccati lattices. We construct exact traveling wave solutions on the basis of the solution of Riccati equation for three members of the class of generalized Holing lattices.
    08/2012; 42(3). DOI:10.2478/v10254-012-0011-2
  • Source
    • "Since the past two decades, a growing interest has been devoted to the dynamics of kinks in strongly dissipative or reaction-diffusion systems [Murray 1989; Nagumo et al., 1962; Keener 2000; Comte et al., 1999; Ferreira et al., 2002]. Indeed, discrete reaction-diffusion equations supporting kink solutions are widely used to describe the excitation spread in a variety of systems in physics, biology or chemistry [Murray 1989; Scott 1999]. "
    [Show abstract] [Hide abstract]
    ABSTRACT: We study the dynamics of a kink propagating in a Nagumo chain presenting a geometrical bifurcation. In the case of weak couplings, we define analytically and numerically the coupling conditions leading to the pinning of the kink at the bifurcation site. Moreover, real experiments using a nonlinear electrical lattice confirm the theoretical and numerical predictions.
    International Journal of Bifurcation and Chaos 01/2004; 14(1):257-262. DOI:10.1142/S0218127404009144 · 1.08 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Nonlinear Systems for Image Processing
Show more