Article

# 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: 2.33). 01/2000; 60(6 Pt B):7484-9. DOI: 10.1103/PhysRevE.60.7484 Source: PubMed

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**ABSTRACT:**A contour detection based on a diffusive cellular nonlinear network is proposed. It is shown that there exists a particular nonlinear function for which, numerically, the obtained contour is satisfactory. Furthermore, this nonlinear function can be achieved using analog components.International Journal of Bifurcation and Chaos 01/2001; 11(01):179-183. · 1.02 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We demonstrate experimentally the compact-like kinks existence in a real electrical reaction–diffusion chain. Our measures show that such entities are strictly localized and consequently present a finite spatial extent. We show equally that the kink velocity is threshold-dependent. A theoretical quantification of the critical coupling under which propagation fails is also achieved and reveals that nonlinear coupling leads to a propagation failure reduction.Chaos Solitons & Fractals 07/2006; 29(2):307-312. · 1.50 Impact Factor -
##### Article: Exact static solutions of a generalized discrete phi4 model including short-periodic solutions

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**ABSTRACT:**We carry out a comprehensive analysis of a generalized discrete phi4 model, of which virtually all phi4 models discussed in the literature are particular cases. For this model we construct the exact solutions in the form of the basic Jacobi elliptic, hyperbolic and sine functions, and also give a list of short-periodic and even aperiodic solutions. Some of those solutions coincide with the known ones, others generalize the existing solutions and the rest of them are new. We then discuss the relation between the models supporting exact static solutions and the two-point maps. In particular, we show that some of the short-periodic and sine solutions can be found from factorized difference equations and even from a set of two difference equations, one of the first and another of the second order. Particular attention is paid to the discussion of the exceptional discrete (ED) models defined as models supporting the translationally invariant (TI) static solutions that can be placed arbitrarily with respect to the lattice. We show that some of the derived short-periodic solutions are TI ones while the others are not. For the TI static solutions we demonstrate the existence of the translational Goldstone mode for any location of the solution with respect to the lattice. We then analyze numerically the stability and other properties of the TI kink solutions. In conclusion, we divide the ED models into two classes: the ED I models support a two-parameter set of TI static solutions, while the ED II models support only a one-parameter set of such solutions.Journal of Physics A Mathematical and Theoretical 04/2009; 42(14). · 1.77 Impact Factor

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