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.