Bakrani, SajjadLamb, Jeroen S. W.Turaev, Dmitry2023-10-192023-10-19202200022-03961090-2732https://doi.org/10.1016/j.jde.2022.04.002https://hdl.handle.net/20.500.12469/5060We consider a Z(2)-equivariant flow in 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 Schrodinger equations is considered. (C) 2022 The Authors. Published by Elsevier Inc.eninfo:eu-repo/semantics/openAccessSystemsClassificationSaddleHomoclinicSystemsSuper-homoclinicClassificationInvariant manifoldSaddleCoupled Schrodinger equationsArticle163327WOS:00081992970000110.1016/j.jde.2022.04.0022-s2.0-85129075632Q1Q1