  We use Riemann problem for soliton gas as a benchmark for a detailed
numerical validation of the spectral kinetic theory for the Korteweg-de Vries
(KdV) and the focusing nonlinear Schr\"odinger (fNLS) equations. We construct
weak solutions to the kinetic equation for soliton gas describing collision of
two dense "polychromatic" soliton gases composed of a finite number of
"monochromatic" components, each consisting of solitons with nearly identical
spectral parameters of the scattering operator in the Lax pair. The interaction
between the gas components plays the key role in the emergent, large-scale
hydrodynamic evolution. We then use the solutions of the spectral kinetic
equation to evaluate macroscopic physical observables in KdV and fNLS soliton
gases and compare them with the respective ensemble averages extracted from the
"exact" soliton gas numerical solutions of the KdV and fNLS equations. To
numerically synthesise dense polychromatic soliton gases we develop a new
method which combines recent advances in the spectral theory of the so-called
soliton condensates and the effective algorithms for the numerical realisation
of $n$-soliton solutions with large $n$.
