  We consider a (mathbb{Z}_2)-equivariant flow in (mathbb{R}^{4}) with an
integral of motion and a hyperbolic equilibrium with a transverse homoclinic
orbit (Gamma). We provide criteria for the existence of stable and unstable
invariant manifolds of (Gamma). We prove that if these manifolds intersect
transversely, creating a so-called super-homoclinic, then in any neighborhood
of this super-homoclinic there exist infinitely many multi-pulse homoclinic
loops. An application to a system of coupled nonlinear Schr\"odinger equations
is considered.
