Stability of multi-parameter solitons: asymptotic approach

Dmitry V. Skryabin

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

A general asymptotic approach to the stability problem of multi-parameter solitons in Hamiltonian systems has been developed. The presented approach gives an analytical criterion for oscillatory instability and also predicts novel stationary instability of solitons. Higher order approximations allow one to calculate corresponding eigenvalues with an arbitrary accuracy. It is also shown that asymptotic study of the soliton stability reduces 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 is just the first in the series.
LanguageEnglish
Pages186-193
Number of pages8
JournalPhysica D: Nonlinear Phenomena
Volume139
Issue number1-2
DOIs
Publication statusPublished - 1 May 2000

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solitary waves
determinants
eigenvalues
matrices
approximation

Keywords

  • multi-parameter solitons
  • solitons
  • instability
  • oscillatory instability

Cite this

Skryabin, Dmitry V. / Stability of multi-parameter solitons : asymptotic approach. In: Physica D: Nonlinear Phenomena. 2000 ; Vol. 139, No. 1-2. pp. 186-193.
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Stability of multi-parameter solitons : asymptotic approach. / Skryabin, Dmitry V.

In: Physica D: Nonlinear Phenomena, Vol. 139, No. 1-2, 01.05.2000, p. 186-193.

Research output: Contribution to journalArticle

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AB - A general asymptotic approach to the stability problem of multi-parameter solitons in Hamiltonian systems has been developed. The presented approach gives an analytical criterion for oscillatory instability and also predicts novel stationary instability of solitons. Higher order approximations allow one to calculate corresponding eigenvalues with an arbitrary accuracy. It is also shown that asymptotic study of the soliton stability reduces 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 is just the first in the series.

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KW - instability

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