## Abstract

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 language | English |
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Pages (from-to) | 107-112 |

Number of pages | 6 |

Journal | Physics Letters A |

Volume | 180 |

Issue number | 1-2 |

Publication status | Published - 30 Aug 1993 |