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 language | English (US) |
|---|---|
| Article number | 016213 |
| Pages (from-to) | 162131-1621312 |
| Number of pages | 1459182 |
| Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |
| Volume | 68 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jul 2003 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics