  The Euler equations describing two-dimensional steady flows of an inviscid
fluid are studied. These equations are reduced to one equation for the stream
function and then, using the Hirota function, solutions of three nonlinear
elliptic equations are found. %: Sine-Gordon, Sinh-Gordon and Tzitz\'{e}ica.
The solutions found are interpreted as sources in a rotating fluid, jets,
chains of sources and sinks, vortex structures. We propose a new simple method
for constructing solutions in the form of rational expressions of elliptic
functions. It is shown that the flux of fluid across a closed curve is
quantized in the case of the elliptic Sin-Gordon equation.
