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

E. A. Kuznetsov

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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, Section A: General, Atomic and Solid State Physics
Issue number31
Publication statusPublished - 10 Aug 2018


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


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