High order Melnikov method: Theory and application

Fengjuan Chen, Qiudong Wang

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Let D(t 0 ,ε) be the splitting distance of the stable and unstable manifold of a time-periodic second order equation. We expand D(t 0 ,ε) as a formal power series in ε as D(t 0 ,ε)=E 0 (t 0 )+εE 1 (t 0 )+⋯+ε n E n (t 0 )+⋯. In this paper we derive an explicit integral formula for E 1 (t 0 ). We also evaluate E 1 (t 0 ) to prove the existence of homoclinic tangles for an equation to which the Poincaré/Melnikov method fails to apply.

Original languageEnglish (US)
Pages (from-to)1095-1128
Number of pages34
JournalJournal of Differential Equations
Issue number2
StatePublished - Jul 5 2019


  • High order Melnikov method
  • Homoclinic intersection
  • Time periodic equation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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