NONLINEAR ACOUSTICS IN GALILEAN AND RELATIVISTIC BAROTROPIC FLUIDS

Non-linear waves described by the defocusing non-linear Schroedinger ( NLS) equation admit a hydrodynamical representation in terms of Galile an potential Bows and, using this correspondence, an autonomous equati on for potential Bow's non-linear acoustic has been recently derived b y Nore et al. However, this equation does not contain simple solutions of the original one such as (dark) solitons. The purpose of the prese nt article is to characterize the reasons behind this failure and to p resent an original method to build separate equations describing all d ifferent types of acoustic solutions (but one). For reasons of general ity, we work in a framework adapted to special relativistic hydrodynam ics. All the results we derive have Galilean counterparts which are al so discussed. In particular, we argue that there exist an infinity of different acoustic sectors for relativistic barotropic fluids, and we prove this result for fluids with a particularly simple equation of st ate. Solitons are naturally captured by our approach and a few explici t examples are worked out. Conserved quantities for the acoustic regim e are also derived.