Hydrodynamic profiles and constants of motion fromd-Branes

Various hydrodynamic systems, governed by nonlinear differential equations, have a hidden higher-dimensional dynamic Poincaré symmetry because the governing equations descend from a Nambu-Goto action. For the same reason, there are also equivalence transformations between different models. We discuss these interconnections and summarize them in a simple diagram. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 124, pp. 215–226. August, 2000