  We analytically study the long time and large space asymptotics of a new
broad class of solutions of the KdV equation introduced by Dyachenko, Zakharov,
and Zakharov. These solutions are characterized by a Riemann--Hilbert problem
which we show arises as the limit $N\to \infty$ of a gas of $N$-solitons. We
show that this gas of solitons in the limit $N \to \infty$ is slowly
approaching a cnoidal wave solution for $x \to - \infty$ (up to terms of order
$\mathcal{O} (1/x)$), while approaching zero exponentially fast for
$x\to+\infty$. We establish an asymptotic description of the gas of solitons
for large times that is valid over the entire spatial domain, in terms of
Jacobi elliptic functions.
