Analysis of stability of solitons in one-dimensional lattices

Nikos Flytzanis, Boris A. Malomed, Jonathan A D Wattis

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We develop a direct analysis of the soliton stability problem for the simplest model of a closed dynamical lattice with the potential of the nearest-neighbor interaction containing quadratic and quartic terms. In the lowest approximation the soliton is represented as a discrete step function, its height being an arbitrary parameter. In this approximation, the stability problem is solved analytically. The soliton proves to be always stable; a single localized eigenmode of small disturbances is found, all other eigenmodes being delocalized. In the next approximation, the soliton is taken as a combination of two steps, so that it has an inner degree of freedom. Using numerical methods, we demonstrate that in this approximation the soliton remains stable; a second localized eigenmode is found in a certain parametric region. © 1993.

Original languageEnglish
Pages (from-to)107-112
Number of pages6
JournalPhysics Letters A
Issue number1-2
Publication statusPublished - 30 Aug 1993

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    Flytzanis, N., Malomed, B. A., & Wattis, J. A. D. (1993). Analysis of stability of solitons in one-dimensional lattices. Physics Letters A, 180(1-2), 107-112.