Localized solutions in parametrically driven pattern formation

Tae Chang Jo, Hans Armbruster

Research output: Contribution to journalArticle

Abstract

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
Volume68
Issue number1
DOIs
StatePublished - 2003

Fingerprint

Pattern Formation
Solitons
Partial differential equation
solitary waves
Parametric Resonance
partial differential equations
Soliton Solution
Perturbation Theory
Forcing
Damping
Nonlinear Equations
Unstable
Perturbation
nonlinear equations
perturbation theory
damping
perturbation
Model

ASJC Scopus subject areas

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

Cite this

Localized solutions in parametrically driven pattern formation. / Jo, Tae Chang; Armbruster, Hans.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 68, No. 1, 016213, 2003, p. 162131-1621312.

Research output: Contribution to journalArticle

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