  We develop three asymptotic models of surface waves in a non-newtonian fluid
with odd viscosity. This viscosity is also known as Hall viscosity and appears
in a number of applications such as quantum Hall fluids or chiral active
fluids. Besides the odd viscosity effects, these models capture both gravity
and capillary forces up to quadratic interactions and take the form of
nonlinear and nonlocal wave equations. Two of these models describe
bidirectional waves while the third PDE studies the case of unidirectional
propagation. We also prove the well-posedness of these asymptotic models in
spaces of analytic functions and in Sobolev spaces. Finally, we present a
number of numerical simulations for the unidirectional model.
