Existence of traveling waves in Fermi-Pasta-Ulam-type systems on a 2D-lattice

DOI10.1007/S10958-020-05173-6zbMath1464.34030OpenAlexW3121098148MaRDI QIDQ2226897

S. M. Bak, G. M. Kovtonyuk

Publication date: 9 February 2021

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-020-05173-6

zbMATH Keywords

critical point theorytraveling waves2D-latticeFermi-Pasta-Ulam systems

Mathematics Subject Classification ID

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

Related Items (5)

Well-posedness of the Cauchy problem for system of oscillators on 2D-lattice in weighted \(L^2\)-spaces ⋮ Existence of periodic traveling waves in Fermi-Pasta-Ulam type systems on 2D-lattice with saturable nonlinearities ⋮ Periodic traveling waves in Fermi-Pasta-Ulam type systems with nonlocal interaction on 2D-lattice ⋮ Existence of traveling solitary waves in Fermi-Pasta-Ulam-type systems with saturable nonlinearities on 2D-lattice ⋮ Unnamed Item

Cites Work

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• Traveling waves in systems of oscillators on 2D-lattices
• Existence of periodic travelling waves in Fermi-Pasta-Ulam system on 2D-lattice
• Existence of periodic traveling waves in a system of nonlinear oscillators on a two-dimensional lattice
• Breathers in nonlinear lattices: existence, linear stability and quantization
• Existence of solitary traveling waves in a system of nonlinearly coupled oscillators on the 2D lattice
• Geometric solitary waves in a 2D mass-spring lattice
• Minimax theorems
• Global well-posedness of the Cauchy problem for a system of oscillators on a 2D-lattice with power potentials
• Existence of standing waves in DNLS with saturable nonlinearity on 2D-lattice
• Homoclinic traveling waves in discrete sine-Gordon equation with nonlinear interaction on 2D-lattice
• Existence of solitary traveling waves in Fermi-Pasta-Ulam system on 2D-lattice
• Travelling waves in Hamiltonian systems on 2D lattices with nearest neighbour interactions

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