Abstract
We consider bifurcation of steady states from a trivial solution of PDEs. The existence of arbitrarily high corank bifurcation points is shown to be generic in restrictions of PDEs with Euclidean equivariance to systems periodic on rectangular (or rhombic) lattices under certain rationality assumptions. As an example, we examine the Kuramoto-Sivashinsky equation on a rectangular domain with Neumann boundary conditions, using Liapunov-Schmidt reduction in a two parameter setting.
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© 1992 Birkhäuser Verlag Basel
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Ashwin, P. (1992). High Corank Steady-State Mode Interactions on a Rectangle. In: Allgower, E.L., Böhmer, K., Golubitsky, M. (eds) Bifurcation and Symmetry. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 104. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7536-3_3
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DOI: https://doi.org/10.1007/978-3-0348-7536-3_3
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