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Bifurcation theory in the context of nonlinear steady water waves

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SIP - Mathematics of sea ice phenomena

Global bifurcation theory is the most successful method for proving existence of fully nonlinear steady water waves of large amplitude. I will present an overview of some of the most significant results in abstract bifurcation theory (the Crandall—Rabinowitz local bifurcation theorem, the global topological theories of Rabinowitz and of Kielhofer, and the global real-analytic theory of Dancer, Buffoni and Toland), together with some aspects concerning the application of these results in the context of various types of steady nonlinear water waves (gravity waves, capillary-gravity waves, and waves beneath an elastic ice sheet).

This talk is part of the Isaac Newton Institute Seminar Series series.

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