  Dynamical equations in generalized hydrodynamics (GHD), a hydrodynamic theory
for integrable quantum systems at the Euler scale, take a rather simple form,
even though an infinite number of conserved charges are taken into account. We
show a remarkable quantum-classical equivalence: we demonstrate the equivalence
between the equations of GHD, and the Euler-scale hydrodynamic equations of a
new family of classical gases which generalize the gas of hard rods. In this
family, the "quasi-particles", upon colliding, jump forward or backward by a
distance that depends on their velocities, generalizing the jump forward by the
rods' length of the fixed-velocity tracer upon elastic collision of two hard
rods. Such velocity-dependent position shifts are characteristics of classical
soliton scattering. The emerging hydrodynamics of a quantum integrable model is
therefore that of the classical gas of its solitons. This provides a "molecular
dynamics" for GHD which is numerically efficient and flexible. This is directly
applicable, for instance, to the study of inhomogeneous dynamics in integrable
quantum chains and in the Lieb-Liniger model realized in cold-atom experiments.
