Localized solutions in parametrically driven pattern formation

Tae Chang Jo, Hans Armbruster

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


An analysis of Mathieu partial differential equation (PDE) as a prototypical model for pattern formation due to parametric resonance, was presented. It was shown that Mathieu PDE was a perturbed nonlinear Schrödinger (NLS) equation. To determine which solitons of the NLS survived the perturbation due to damping and parametric forcing adiabatic perturbation theory of solitons was used. Weakly unstable and stable soliton solutions were identified.

Original languageEnglish (US)
Article number016213
Pages (from-to)162131-1621312
Number of pages1459182
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number1 2
StatePublished - Jul 1 2003

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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