Existence of Bounded Soliton Solutions in the Problem of Longitudinal Vibrations of an Infinite Elastic Rod in a Field with a Strongly Nonlinear Potential
Leva Andreevich Beklaryan, Armen L. Beklaryan · Computational Mathematics and Mathematical Physics · 2021
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.