  There have been several existence results for the standing waves of
FitzHugh-Nagumo equations. Such waves are the connecting orbits of an
autonomous second-order Lagrangian system and the corresponding kinetic energy
is an indefinite quadratic form in the velocity terms. When the system has two
stable hyperbolic equilibria, there exist two stable standing fronts, which
will be used in this paper as building blocks, to construct stable standing
waves with multiple fronts in case the equilibria are of saddle-focus type. The
idea to prove existence is somewhat close in spirit to [Buffoni-Sere, CPAM 49,
285-305]. However several differences are required in the argument: facing a
strongly indefinite functional, we need to perform a nonlo-cal Lyapunov-Schmidt
reduction; in order to justify the stability of multiple front standing waves,
we rely on a more precise variational characterization of such critical points.
Based on this approach, both stable and unstable standing waves are
established.
