Poles and Branch Cuts in Free Surface Hydrodynamics

@article{Lushnikov2019PolesAB,
  title={Poles and Branch Cuts in Free Surface Hydrodynamics},
  author={Pavel M. Lushnikov and V. E. Zakharov},
  journal={Water Waves},
  year={2019},
  volume={3},
  pages={251-266}
}
We consider the motion of ideal incompressible fluid with free surface. We analyzed the exact fluid dynamics through the time-dependent conformal mapping $$z=x+iy=z(w,t)$$ z = x + i y = z ( w , t ) of the lower complex half plane of the conformal variable w into the area occupied by fluid. We established the exact results on the existence vs. nonexistence of the pole and power law branch point solutions for $$1/z_w$$ 1 / z w and the complex velocity. We also proved the nonexistence of the time… 
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