  The purpose of this paper is to explain the phenomenon of symmetry breaking
for optimal functions in functional inequalities by the numerical computations
of some well chosen solutions of the corresponding Euler-Lagrange equations.
For many of those inequalities it was believed that the only source of symmetry
breaking would be the instability of the symmetric optimizer in the class of
all admissible functions. But recently, it was shown by an indirect argument
that for some Caffarelli-Kohn-Nirenberg inequalities this conjecture was not
true. In order to understand this new symmetry breaking mechanism we have
computed the branch of minimal solutions for a simple problem. A
reparametrization of this branch allows us to build a scenario for the new
phenomenon of symmetry breaking. The computations have been performed using
Freefem++.
