The Regularity and Local Bifurcation of¶Steady Periodic Water Waves

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Steady Periodic Water Waves with Constant Vorticity: Regularity and Local Bifurcation (2009, background): “A more recent approach [5, 6, 31] (for the analogous problem of waves of infinite depth) uses a reformulation of the problem as a pseudodifferential equation for a function of one variable which gives the elevation of the free surface when the fluid domain is the conformal image of a strip [2].”
Convexity of Stokes Waves of Extreme Form (2004, background): “However if E is the subset of C1=3 which is obtained from real-analytic global bifurcation theory (see [4, 5 , 6] for details), then E is a curve in (0;1=3] £ Z with the property that”
Dynamics and bifurcations of nonsmooth systems: A survey (2012, background): “equation (see Buffoni-Dancer-Toland [66]) and construct solutions of these partial differential equations, starting from convenient ordinary differential equations.”
Global bifurcation of steady gravity water waves with critical layers (2014, background): “As mentioned in the introduction, it could be regarded as an analogue of Babenko’s formulation [2] for the irrotational water-wave problem of infinite depth, which has turned out to be instrumental in the recent theory of global and subharmonic bifurcation in the irrotational infinite-depth case [3,”