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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 12, Pages 2024–2039
DOI: https://doi.org/10.31857/S0044466921120061 (Mi zvmmf11328) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Partial Differential Equations

Existence of bounded soliton solutions in the problem of longitudinal vibrations of an infinite elastic rod in a field with a strongly nonlinear potential

L. A. Beklaryana, A. L. Beklaryanb

a Central Economics and Mathematics Institute, Russian Academy of Sciences, 117418, Moscow, Russia
b National Research University Higher School of Economics, 101000, Moscow, Russia
Citations (2)
DOI: https://doi.org/10.31857/S0044466921120061
Abstract: The existence of a family of bounded soliton solutions for a finite-difference wave equation with a quadratic potential is established. The proof is based on a formalism establishing a one-to-one correspondence between the soliton solutions of an infinite-dimensional dynamical system and the solutions of a family of functional differential equations of the pointwise type. A key point for the considered class of equations is also the existence of a number of symmetries.
Key words: wave equation, soliton solutions, nonlinear potential.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00147
This work was supported by the Russian Foundation for Basic Research, project no. 19-01-00147.
Received: 22.12.2020
Revised: 07.04.2021
Accepted: 04.08.2021
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 12, Pages 1980–1994
DOI: https://doi.org/10.1134/S0965542521120058
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: L. A. Beklaryan, A. L. Beklaryan, “Existence of bounded soliton solutions in the problem of longitudinal vibrations of an infinite elastic rod in a field with a strongly nonlinear potential”, Zh. Vychisl. Mat. Mat. Fiz., 61:12 (2021), 2024–2039; Comput. Math. Math. Phys., 61:12 (2021), 1980–1994
Citation in format AMSBIB
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