We show that the Vlasov and Euler equations can be transformed into each other along the same characteristics on the (x, t) plane. Therefore, the Vlasov-Poisson plasma may have common features that are contained in the cold fluid equations: the Euler equation, the continuity equation, and the Poisson equation. Here, the cold fluid equation does not mean the moment equation of the Boltzmann equation. We show that the compensated electron fluid equations can be solved linearly along the characteristics. We address an ion plasma with Boltzmann-distributed electrons as a Cauchy initial-boundary value problem for which initial data are provided by compatible solutions of the Poisson equation. In this plasma, the set of nonlinear cold fluid equations can be approached by arranging them in Riemann invariant equations or via a hodograph transform. The result of this arrangement is linear equations, thus suggesting a way to investigate a cold fluid nonlinear plasma without directly engaging the nonlinearity. The Poisson equation corresponds to the entropy equation in the gas dynamic equations. Analogously, a power law similar to the polytropic gas law in gas dynamics is assumed between the electric potential and the density.