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

- [Show abstract] [Hide abstract]

**ABSTRACT:**We report some ideas for constructing lattice models (LMs) as a discrete approach to the reaction-dispersal (RD) or reaction-random walks (RRW) models. The analysis of a rather general class of Markovian and non-Markovian processes, from the point of view of their wavefront solutions, let us show that in some regimes their macroscopic dynamics (front speed) turns out to be different from that by classical reaction–diffusion equations, which are often used as a mean-field approximation to the problem. So, the convenience of a more general framework as that given by the continuous-time random walks (CTRW) is claimed. Here we use LMs as a numerical approach in order to support that idea, while in previous works our discussion was restricted to analytical models. For the two specific cases studied here, we derive and analyze the mean-field expressions for our LMs. As a result, we are able to provide some links between the numerical and analytical approaches studied.Journal of Physics A Mathematical and Theoretical 01/2008; 4120:5-70. · 1.77 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**In this letter, we use the method of constructing exact solutions on lattices proposed by Kinnersley and described in Schmidt (1979 Phys. Rev. B 20 4397), to obtain exact compacton solutions in discrete models. We examine the linear stability of such solutions, both for the bright compacton and for the dark compacton cases. We focus on a 'quantization condition' that the width of the profile should satisfy. We also use this quantization condition to examine the possibility of compact coherent structures travelling in discrete settings. Our results are obtained for sinusoidal profiles and then generalized to elliptic functions of arbitrary modulus. The possibility of multi-compacton solutions is considered.Journal of Physics A General Physics 10/2002; 35(45):L641. - [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.Journal of Theoretical and Applied Mechanics. 08/2012; 42(3).

Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.