Orateur
Description
We investigate the Riemann problem for KdV soliton condensates, where the left and right states are characterized by distinct densities of states associated with two soliton condensates. At the level of physical initial data, this problem may be viewed as a perturbation of a step-like finite-gap background. However, such perturbations lie beyond the scope of the currently available inverse scattering theory for step-like finite-gap potentials, making a direct IST analysis unavailable. In contrast to previously studied configurations, we allow the spectral bands of the left and right condensates to overlap. The resulting overlap region represents a full soliton gas and produces a new intermediate asymptotic region in which the leading-order term is a genus-one finite-gap solution with fixed spectral data but a nontrivially modulated phase. Such a phenomenon does not occur in the non-overlapping regime.