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Existence of traveling waves in Fermi-Pasta-Ulam-type systems on a 2D-lattice. (English. Ukrainian original) Zbl 1464.34030

J. Math. Sci., New York 252, No. 4, 453-462 (2021); translation from Ukr. Mat. Visn. 17, No. 3, 301-312 (2020).
The authors investigate the Fermi-Pasta-Ulam-type systems of particles on an infinite two-dimensional lattice. The mountain pass theorem is applied to find sufficient conditions for the existence of periodic wave solutions and solitary wave solutions, respectively.

MSC:

34A33 Ordinary lattice differential equations
34C25 Periodic solutions to ordinary differential equations
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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