[1] Aubry, S.: Breathers in nonlinear lattices: existence, linear stability and quantization. Physica D 103 (1997), 201–250. DOI 10.1016/S0167-2789(96)00261-8

[2] Bak, S.: The existence of heteroclinic traveling waves in the discrete sine-Gordon equation with nonlinear interaction on a 2D-lattice. Zh. Mat. Fiz. Anal. Geom. 14 (1) (2018), 16–26. DOI 10.15407/mag14.01.016 | MR 3783757

[3] Bak, S.M.: Travelling waves in chains of oscillators. Mat. Stud. 26 (2) (2006), 140–153. MR 2314304

[4] Bak, S.M.: Periodic travelling waves in chains of oscillators. Commun. Math. Anal. 3 (1) (2007), 19–26. MR 2347772

[5] Bak, S.M.: Existence of periodic traveling waves in systems of nonlinear oscillators on 2D-lattice. Mat. Stud. 35 (1) (2011), 60–65, (in Ukrainian). MR 2816218

[6] Bak, S.M.: Periodic travelling waves in the discrete sine–Gordon equation on 2D-lattice. Math. Comput. Model. Phys. Math. Sci. 9 (2013), 5–10, (in Ukrainian).

[7] Bak, S.M.: Existence of heteroclinic traveling waves in a system of oscillators on a two-dimensional lattice. J. Math. Sci. 217 (2) (2016), 187–197. DOI 10.1007/s10958-016-2966-z | MR 3532455

[8] Bak, S.M.: Existence of solitary traveling waves for a system of nonlinearly coupled oscillators on the 2d-lattice. Ukr. Math. J. 69 (4) (2017), 509–520. DOI 10.1007/s11253-017-1378-7 | MR 3655283

[9] Bak, S.M.: Homoclinic travelling waves in discrete sine-Gordon equation with nonlinear interaction on 2D lattice. Mat. Stud. 52 (2) (2019), 176–184. MR 4056523

[10] Bak, S.N., Pankov, A.A.: Travelling waves in systems of oscillators on 2D-lattices. J. Math. Sci. 174 (4) (2011), 916–920. MR 2768150

[11] Bell, J.: Some threshold results for models of myelinated nerves. Math. Biosci. 54 (1981), 181–190. DOI 10.1016/0025-5564(81)90085-7

[12] Braun, O.M., Kivshar, Y.S.: Nonlinear dynamics of the Frenkel-Kontorova model. Phys. Rep. 306 (1998), 1–108. DOI 10.1016/S0370-1573(98)00029-5

[13] Braun, O.M., Kivshar, Y.S.: The Frenkel-Kontorova Model. Concepts, Methods and Applications. Berlin: Springer, 2004. MR 2035039

[14] Cahn, J.W.: Theory of crystal growth and interface motion in crystalline materials. Acta Metall. 8 (1960), 554–562. DOI 10.1016/0001-6160(60)90110-3

[15] Cahn, J.W., Mallet-Paret, J., van Vleck, E.S.: Travelling wave solutions for systems of ODEs on a two-dimensional spatial lattice. SIAM J. Appl. Math. 59 (2) (1998), 455–493. DOI 10.1137/S0036139996312703

[16] Chow, S.N., Mallet-Paret, J., Shen, W.: Travelling waves in lattice dynamical systems. J. Differential Equations 149 (1998), 248–291. DOI 10.1006/jdeq.1998.3478

[17] Chua, L.O., Roska, T.: The CNN paradigm. IEEE Trans. Circuits Syst. 40 (1993), 147–156. DOI 10.1109/81.222795

[18] Eilbeck, J.C., Flesch, R.: Calculation of families of solitary waves on discrete lattices. Phys. Lett. A 149 (1990), 200–202. DOI 10.1016/0375-9601(90)90326-J

[19] Fečkan, M., Rothos, V.: Travelling waves in Hamiltonian systems on 2D lattices with nearest neighbour interactions. Nonlinearity 20 (2007), 319–341. DOI 10.1088/0951-7715/20/2/005 | MR 2290465

[20] Flach, S., Willis, C.R.: Discrete breathers. Phys. Rep. 295 (1998), 181–264. DOI 10.1016/S0370-1573(97)00068-9

[21] Friesecke, G., Matthies, K.: Geometric solitary waves in a 2D math-spring lattice. Discrete Contin. Dyn. Syst. 3 (1) (2003), 105–114. MR 1951571

[22] Hupkes, H.J., Morelli, L., Stehlí, P., Švígler, V.: Multichromatic travelling waves for lattice Nagumo equations. Appl. Math. Comput. 361 (15) (2019), 430–452. MR 3961829

[23] Iooss, G., Kirschgässner, K.: Travelling waves in a chain of coupled nonlinear oscillators. Commun. Math. Phys. 211 (2000), 439–464. DOI 10.1007/s002200050821

[24] Keener, J.P.: Propagation and its failure in coupled systems of discrete excitable cells. SIAM J. Appl. Math. 47 (3) (1987), 556–572. DOI 10.1137/0147038

[25] Kreiner, C.-F., Zimmer, J.: Heteroclinic travelling waves for the lattice sine-Gordon equation with linear pair interaction. Discrete Contin. Dyn. Syst. 25 (3) (2009), 1–17. MR 2533982

[26] Kreiner, C.-F., Zimmer, J.: Travelling wave solutions for the discrete sine-Gordon equation with nonlinear pair interaction. Nonlinear Anal. 70 (9) (2009), 3146–3158. DOI 10.1016/j.na.2008.04.018 | MR 2503060

[27] Laplante, J.P., Erneux, T.: Propagation failure in arrays of coupled bistable chemical reactors. J. Phys. Chem. 96 (1992), 4931–4934. DOI 10.1021/j100191a038

[28] Makita, P.D.: Periodic and homoclinic travelling waves in infinite lattices. Nonlinear Anal. 74 (2011), 2071–2086. DOI 10.1016/j.na.2010.11.011 | MR 2781738

[29] Pankov, A.: Traveling waves and periodic oscillations in Fermi-Pasta-Ulam lattices. London: Imperial College Press, 2005. MR 2156331

[30] Rabinowitz, P.H.: Minimax methods in critical point theory with applications to differential equations. CBMS Regional Conference Series in Mathematics, American Mathematical Society, Providence, RI, 1986. Zbl 0609.58002

[31] Wattis, J.A.D.: Approximations to solitary waves on lattices, II: Quasicontinuum methods for fast and slow waves. J. Phys. A 26 (1993), 1193–1209. DOI 10.1088/0305-4470/26/5/036

[32] Wattis, J.A.D.: Solitary waves on a two-dimensional lattice. Phys. Scripta 50 (3) (1994), 238–242. DOI 10.1088/0031-8949/50/3/003

[33] Wattis, J.A.D.: Approximations to solitary waves on lattices, III: The monatomic lattice with second-neighbour interactions. J. Phys. A 29 (1996), 8139–8157. DOI 10.1088/0305-4470/29/24/035

[34] Willem, M.: Minimax theorems. Boston, Birkhäuser, 1996. Zbl 0856.49001

[35] Zhang, L., Guo, S.: Existence and multiplicity of wave trains in 2D lattices. J. Differential Equations 257 (2014), 759–783. DOI 10.1016/j.jde.2014.04.016 | MR 3208090