Abstract
The existence of a family of bounded soliton solutions for a finite-difference analogue of the wave equation with a general nonlinear potential is proved. The proof is based on a formalism establishing a one-to-one correspondence between soliton solutions of an infinite-dimensional dynamical system and solutions of a family of functional differential equations of the pointwise type. A key point in the proof of the existence of bounded soliton solutions is a theorem on the existence and uniqueness of soliton solutions in the case of a quasilinear potential. Another important circumstance for the considered class of systems of equations is that they have a number of symmetries due to the low dimension (one-dimensionality) of the space at each lattice point.
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The work was supported by the Russian Foundation for Basic Research, project no. 19-01-00147.
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Beklaryan, A.L., Beklaryan, L.A. Existence of Bounded Soliton Solutions in the Problem of Longitudinal Oscillations of an Elastic Infinite Rod in a Field with a Nonlinear Potential of General Form. Comput. Math. and Math. Phys. 62, 904–919 (2022). https://doi.org/10.1134/S0965542522060033
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DOI: https://doi.org/10.1134/S0965542522060033