Dislocations in an anisotropic Swift-Hohenberg equation

Mariana Haragus (1) , Arnd Scheel (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 UMN-MATH - School of Mathematics

We study the existence of dislocations in an anisotropic Swift-Hohenberg equation. We find dislocations as traveling or standing waves connecting roll patterns with different wavenumbers in an infinite strip. The proof is based on a bifurcation analysis. Spatial dynamics and center-manifold reduction yield a reduced, coupled-mode system of differential equations. Existence of traveling dislocations is then established by showing that this reduced system possesses robust heteroclinic orbits.

Mots clés: Swift-Hohenberg equation; Roll solution; Dislocation

Domaines: Equations aux dérivées partielles [math.AP]

Mariana Haragus, Arnd Scheel. Dislocations in an anisotropic Swift-Hohenberg equation. Comm. Math. Phys., 2012, 315, pp.311-335. ⟨hal-00472227⟩