DOI:
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A. Abbondandolo and P. Majer, Ordinary differential operators in Hilbert spaces and Fredholm pairs, Math. Z. 243 (2003), 525–562.
J. Alexander, R. Gardner and C. Jones, A topological invariant arising in the stability analysis of travelling waves, J. Reine Angew. Math. 410 (1990), 167–212.
M.F. Atiyah, V.K. Patodi and I.M. Singer, Spectral asymmetry and Riemannian geometry III, Math. Proc. Cambridge Philos. Soc. 79 (1976), no. 1, 71–99.
S.E. Cappell, R. Lee and E.Y. Miller, On the Maslov index, Comm. Pure Appl. Math. 47 (1994), no. 2, 121–186.
F. Chardard, F. Dias and T.J. Bridges, Computing the Maslov index of solitary waves. I. Hamiltonian systems on a four-dimensional phase space, Physica D. Nonlinear Phenomena 238 (2009), no. 18, 1841–1867.
C.-N. Chen and X. Hu, Maslov index for homoclinic orbits of Hamiltonian systems, Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (2007), no. 4, 589–603.
C.-N. Chen and X. Hu, Stability snalysis for standing pulse solutions to FitzHugh–Nagumo equations, Calc. Var. Partial Differential Equations 49 (2014), no. 1–2, 827–845.
P. Cornwell, Opening the Maslov box for traveling waves in skew-gradient systems: counting eigenvalues and proving (in)stability, Indiana Univ. Math. J. 68 (2019), no. 6, 1801–1832.
P. Cornwell and C.K.R.T. Jones, On the existence and stability of fast traveling waves in a doubly diffusive FitzHugh–Nagumo system, SIAM J. Appl. Dyn. Syst. 17 (2018), no. 1, 754–787.
J.J. Duistermaat, On the Morse index in variational calculus, Adv. Math. 21 (1976), no. 2, 173–195.
X. Hu and A. Portaluri, Index theory for heteroclinic orbits of Hamiltonian systems, Calc. Var. Partial Differential Equations 56 (2017), no. 6, paper no. 167, 24 pp.
X. Hu and A. Portaluri, Bifurcation of heteroclinic orbits via an index theory, Math. Z. 292 (2019), no. 1–2, 705–723.
X. Hu, A. Portaluri, L. Wu and Q. Xing, Morse index theorem for heteroclinic orbits of Lagrangian systems, (Apr. 18, 2020), arXiv: 2004.08643 [math].
T. Kapitula and K. Promislow, Spectral and Dynamical Stability of Nonlinear Waves, vol. 185, Applied Mathematical Sciences, New York, NY, Springer New York, 2013.
[H. McKean, Nagumos equation, Adv. Math. 4 (June 1970), no. 3, 209–223.
J. Pejsachowicz, Bifurcation of homoclinics, Proc. Amer. Math. Soc. 136 (2008), no. 1, 111–118.
J. Robbin and D. Salamon, The Maslov index for paths, Topology 32 (October 1993), no. 3, 827–844.
Y. Zhou, L. Wu and C. Zhu, Hörmander index in finite-dimensional case, Front. Math. China 13 (2018), no. 3, 725–761.
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