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Interfaces between rolls in the Swift-Hohenberg equation. (English) Zbl 1169.35032

Authors’ abstract: We study the existence of interfaces between stripe or roll solutions in the Swift-Hohenberg equation. We prove the existence of two different types of interfaces: corner-like interfaces, also referred to as knee solutions, and step-like interfaces. The analysis relies upon a spatial dynamics formulation of the existence problem and an equivariant centre-manifold reduction. In this setting, the interfaces are found as heteroclinic and homoclinic orbits of a reduced system of ODEs.

MSC:

35K55 Nonlinear parabolic equations
35K57 Reaction-diffusion equations
37L10 Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems
35Q53 KdV equations (Korteweg-de Vries equations)
37G05 Normal forms for dynamical systems
76E06 Convection in hydrodynamic stability
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
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