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Floquet theory for, and bifurcations from spatially periodic patterns. (English) Zbl 0811.35008

Summary: We consider elliptic systems of PDEs on infinite long cylindrical domains allowing applications such as travelling waves in reaction-diffusion systems of fluid flow in pipes. We develop a method for studying solutions which are close to a given solution \(u_ 0\) which is periodic with respect to the axial variable \(x\). Using spatial Floquet theory we are able to construct a spatial center manifold and to show that all orbitally close solutions can be described by an ODE.

MSC:

35B32 Bifurcations in context of PDEs
35J60 Nonlinear elliptic equations
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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