High order Melnikov method: Pendulums

Ali Oksasoglu, Qiudong Wang

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we present an explicit integral formula for the high order Melnikov function D1(t0) for periodically perturbed pendulum equations. The acquired integral formula is then applied to a specific pendulum equation to offer an example of high frequency perturbation, of which the classical Melnikov function D0(t0) fails to dominate the higher order term εD1(t0).

Original languageEnglish (US)
Pages (from-to)176-208
Number of pages33
JournalJournal of Differential Equations
Volume312
DOIs
StatePublished - Mar 5 2022

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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