August  2001, 1(3): 363-386. doi: 10.3934/dcdsb.2001.1.363

Multi-bump patterns by a normal form approach

1. 

Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, Netherlands

Received  November 2000 Revised  April 2001 Published  May 2001

In this paper the behaviour of small solutions in a reaction-diffusion model problem is studied near a co-dimension 2 point. The normal form theory for reversible vector fields is applied on the stationary part of the reaction- diffusion system. This normal form is reduced to a 3-dimensional ODE that is completely integrable. An explicit expression for the solutions to the ODE and therefore for the reaction-diffusion system is given under certain conditions. These solutions have the same multi-bump pattern as the asymptotically stable stationary multi-bump solutions that were found in the numerical simulations of the full reaction-diffusion system.
Citation: Vivi Rottschäfer. Multi-bump patterns by a normal form approach. Discrete and Continuous Dynamical Systems - B, 2001, 1 (3) : 363-386. doi: 10.3934/dcdsb.2001.1.363
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