Interfaces between rolls in the Swift-Hohenberg equation | Zendy

Mariana Hărăguş | Zendy; Arnd Scheel | Zendy

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Interfaces between rolls in the Swift-Hohenberg equation

Author(s) -

Mariana Hărăguş,

Arnd Scheel

Publication year - 2007

Publication title -

international journal of dynamical systems and differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.16

H-Index - 14

eISSN - 1752-3591

pISSN - 1752-3583

DOI - 10.1504/ijdsde.2007.016510

Subject(s) - mathematics , homoclinic orbit , equivariant map , mathematical analysis , ode , reduction (mathematics) , swift , pure mathematics , geometry , bifurcation , computer science , physics , quantum mechanics , nonlinear system , programming language

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 center manifold reduction. In this setting, the interfaces are found as heteroclinic and homoclinic orbits of a reduced system of ODEs.

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