TY - JOUR

T1 - Analysis of stability of solitons in one-dimensional lattices

AU - Flytzanis, Nikos

AU - Malomed, Boris A.

AU - Wattis, Jonathan A.D.

PY - 1993/8/30

Y1 - 1993/8/30

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0039732263&partnerID=8YFLogxK

U2 - 10.1016/0375-9601(93)90503-R

DO - 10.1016/0375-9601(93)90503-R

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AN - SCOPUS:0039732263

SN - 0375-9601

VL - 180

SP - 107

EP - 112

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 1-2

ER -