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.

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Available from: Patrick Marquié, Nov 24, 2014
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    • "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] . "
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