Eur. Phys. J. B 55, 439-446 (2007)
https://doi.org/10.1140/epjb/e2007-00069-7

Multi-shocks in reaction-diffusion models

Department of Physics, Alzahra University, Tehran, 19938-91167, Iran

Corresponding authors: ^a m_arabsalmani@alzahra.ac.ir - ^b mohamadi@alzahra.ac.ir

Received: 10 October 2006
Revised: 21 December 2006
Published online: 9 March 2007

Abstract

It is shown, concerning equivalent classes, that on a one-dimensional lattice with nearest neighbour interaction, there are only four independent models possessing double-shocks. Evolution of the width of the double-shocks in different models is investigated. Double-shocks may vanish, and the final state is a state with no shock. There is a model for which at large times the average width of double-shocks will become smaller. Although there may exist stationary single-shocks in nearest neighbour reaction diffusion models, it is seen that in none of these models, there exist any stationary double-shocks. Models admitting multi-shocks are classified, and the long period behaviour of multi-shock solutions is also investigated.