Stability of multi-parameter solitons: Asymptotic approach

1999/06/04 by Dmitry V. Skryabin, Skryabin, Dmitry V.
Mathematics · Physics and Astronomy · #Applied mathematics #Computer science #Differential Equations and Numerical Methods #FOS: Physical sciences #Machine learning #Mathematics #Numerical methods for differential equations #Pattern Formation and Solitons (nlin.PS) #Physics #Stability (learning theory) #Statistical physics #nlin.PS #patt-sol

paper · pdf · doi:10.48550/arxiv.patt-sol/9906003

published in arXiv (Cornell University) (Cornell University) · to appear in Physica D

openalex publication_date 1999/06/04 · arxiv created 1999/08/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

General asymptotic approach to the stability problem of multi-parameter solitons in Hamiltonian systems i∂ E_n/∂ z=δH/δE_n^* has been developed. It has been shown that asymptotic study of the soliton stability can be reduced to the calculation of a certain sequence of the determinants, where the famous determinant of the matrix consisting from the derivatives of the system invariants with respect to the soliton parameters is just the first in the series. The presented approach gives first analytical criterion for the oscillatory instability and also predicts novel stationary instability. Higher order approximations allow to calculate corresponding eigenvalues with arbitrary accuracy.

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