  Applying symmetry reduction to a class of $\mathrm{SL}(2,\mathbb
R)$-invariant third-order ODEs, we obtain Abel equations whose general solution
can be parametrised by hypergeometric functions. Particular case of this
construction provides a general parametric solution to the Kudashev equation,
an ODE arising in the Gurevich--Pitaevskii problem, thus giving the first term
of a large-time asymptotic expansion of its solution in the oscillatory
(Whitham) zone.
