Closed Busse balloon for rolls and skew-varicose instability in a Swift-Hohenberg model with nonlinear resonance

Abstract

A Swift-Hohenberg model incorporating a nonlinear resonance is shown to produce stable rolls only in a closed region of the parameter space. This Busse balloon is limited by zigzag and Eckhaus boundaries. A skew-varicose instability outside the balloon also exists. Implications with nonlinear optics and hydrodynamic convection are commented.