# American Institute of Mathematical Sciences

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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