In this article, we apply local bifurcation theory to prove the existence of small-amplitude steady periodic water waves, which propagate over a flat bed with a specified fixed mean-depth, and where the underlying flow has a discontinuous vorticity distribution.
Henry David. Silvia Sastre-Gomez. "Steady periodic water waves bifurcating for fixed-depth rotational flows with discontinuous vorticity." Differential Integral Equations 31 (1/2) 1 - 26, January/February 2018. https://doi.org/10.57262/die/1509041399