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.
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This work was supported by the Russian Foundation for Basic Research, project no. 19-01-00147.
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Translated by I. Ruzanova
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Beklaryan, L.A., Beklaryan, A.L. Existence of Bounded Soliton Solutions in the Problem of Longitudinal Vibrations of an Infinite Elastic Rod in a Field with a Strongly Nonlinear Potential. Comput. Math. and Math. Phys. 61, 1980–1994 (2021). https://doi.org/10.1134/S0965542521120058
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DOI: https://doi.org/10.1134/S0965542521120058