Stability criterion for solitons of the Zakharov–Kuznetsov-type equations

E. A. Kuznetsov

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)

    Abstract

    Early results concerning the linear stability of the solitons in equation of the KDV-type [1] are generalized to solitons describing by the Zakharov–Kuznetsov-type equation. The linear stability criterion for ground solitons in the Vakhitov–Kolokolov form is derived for such equations with arbitrary nonlinearity. For the power nonlinearity the instability criterion coincides with the condition of the Hamiltonian unboundedness from below. The latter represents the main feature for appearance of collapse in such systems.

    Original languageEnglish
    Pages (from-to)2049-2051
    Number of pages3
    JournalPhysics Letters A
    Volume382
    Issue number31
    DOIs
    Publication statusPublished - 10 Aug 2018

    Keywords

    • Linear and Lyapunov stability
    • Soliton
    • Vakhitov–Kolokolov criterion

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