Existence of periodic traveling waves in Fermi-Pasta-Ulam type systems on 2D-lattice with saturable nonlinearities-Reference-Cited by-同舟云学术

Existence of periodic traveling waves in Fermi-Pasta-Ulam type systems on 2D-lattice with saturable nonlinearities

Published:2021-11-12 Issue:4 Volume:18 Page:466-478
ISSN:1810-3200
Container-title:Ukrainian Mathematical Bulletin
language:uk
Short-container-title:UMB

Author:

Bak Sergiy¹,Kovtonyuk Galyna¹

Affiliation:

1. Mykhailo Kotsiubynskyi State Pedagogical University of Vinnytsia, Vinnytsia, Ukraine

Abstract

The Fermi-Pasta-Ulam-type systems with saturable nonlinearities, namely, infinite systems of particles on a two dimensional lattice, have been considered. The main result concerns the existence of traveling-wave solutions with periodic relative displacement profiles. By means of critical point theory, sufficient conditions for the existence of such solutions have been obtained.

Publisher

Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine

Reference27 articles.

1. Arioli, G., & Gazzola, F. (1996). Periodic motion of an infinite lattice of particles with nearest neighbor interaction, Nonlin. Anal., 26(6), 1103–1114. https://doi.org/10.1016/0362-546x(94)00269-n

2. Aubry, S. (1997). Breathers in nonlinear lattices: Existence, linear stability and quantization. Physica D, 103, 201–250. https://doi.org/10.1016/s0167-2789(96)00261-8

3. Bak, S. M. (2020). Discrete infinite-dimensional Hamiltonian systems on a twodimensional lattice. Doctor. thesis. VSPU, Vinnytsia.

4. Bak, S. M. (2019). Global well-posedness of the Cauchy problem for system of oscillators on 2D-lattice with power potentials. Ukr. Math. Bull., 16(4), 465–476; transl. in (2020). J. Math. Sci., 246(5), 593–601. https://doi.org/10.37069/1810-3200-2019-16-4-1

5. Bak, S. M. (2014). Existence of heteroclinic traveling waves in a system of oscillators on a two-dimensional lattice. Mat. Metody ta Fizyko-Mekhanichni Polya, 57(3), 45–52; transl. in (2016). J. Math. Sci., 217(2), 187–197. https://doi.org/10.1007/s10958-016-2966-z

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Existence of traveling solitary waves in Fermi–Pasta–Ulam-type systems with saturable nonlinearities on 2D-lattice;Journal of Mathematical Sciences;2023-02

2. Existence of traveling solitary waves in Fermi-Pasta-Ulam-type systems with saturable nonlinearities on 2D-lattice;Ukrainian Mathematical Bulletin;2023-01-30