Global Solutions and Stability Properties of the 5th Order Gardner Equation

Miguel A. Alejo, Chulkwang Kwak

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In this work, we deal with the initial value problem of the 5th-order Gardner equation in R, presenting the local well-posedness result in H2(R). As a consequence of the local result, in addition to H2-energy conservation law, we are able to prove the global well-posedness result in H2(R). Finally as a direct application, we prove that some globally defined functions, e.g. breather solutions of 5th order Gardner equation, are H2(R) stable.

Original languageEnglish
Pages (from-to)575-621
Number of pages47
JournalJournal of Dynamics and Differential Equations
Issue number1
StatePublished - Mar 2023

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.


  • Breather
  • Global well-posedness
  • Higher order Gardner equation
  • Integrability
  • Stability


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