We consider the generalized hydrodynamics including the recently introduced diffusion term for an initially inhomogeneous state in the Lieb-Liniger model. We construct a general solution to the linearized hydrodynamics equation in terms of the eigenstates of the evolution operator and study two prototypical classes of initial states: delocalized and localized spatially. We exhibit som... https://safeersappliancers.shop/product-category/neff-d65ibe1s0b-60cm-wide-angled-cooker-hood-with-perimeter-extractio/