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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
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.
Received: 22.12.2020 Revised: 07.04.2021 Accepted: 04.08.2021
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
Linking options:
https://www.mathnet.ru/eng/zvmmf11328 https://www.mathnet.ru/eng/zvmmf/v61/i12/p2024
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