  We study the existence of homoclic solutions for reversible Hamiltonian
systems taking the family of differential equations u^4+au^2-u+f(u,b)=0 as a
model. Here f is an analytic function and a, b real parameters. These equations
are important in several physical situations such as solitons and in the
existence of ``finite energy'' stationary states of partial differential
equations. We reduce the problem of computing these orbits to that of finding
the intersection of the unstable manifold with a suitable set and then apply it
to concrete situations. No assumptions of any kind of discrete symmetry is made
and the analysis here developed can be successfully employed in situations
where standard methods fail.
