Analysis of stability of solitons in one-dimensional lattices

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)107-112
Number of pages6
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Issue number1-2
StatePublished - 30 Aug 1993


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