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We consider large-scale dynamics of non-equilibrium dense soliton gas for theKorteweg-de Vries (KdV) equation in the special "condensate" limit. We provethat in this limit the integro-differential kinetic equation for the spectraldensity of states reduces to the $N$-phase KdV-Whitham modulation equationsderived by Flaschka, Forest and McLaughlin (1980) and Lax and Levermore (1983).We consider Riemann problems for soliton condensates and construct explicitsolutions of the kinetic equation describing generalized rarefaction anddispersive shock waves. We then present numerical results for "diluted" solitoncondensates exhibiting rich incoherent behaviours associated with integrableturbulence.

Dispersive hydrodynamics of soliton condensates for the Korteweg-de Vries equation