Exact Solution to the Compressible Euler System in 1-$D^∗$ (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, the exact solution of one-dimensional isentropic Euler equations is studied. When the exponent of the state equation satisfies $γ = 2,$ we get an exact solution which is linear with respect to the spatialvariable $x.$ For this end, we solve some ordinary differential equations withtime dependent variable coefficients.
Keywords: Euler equations; compressible; exact solutions; ordinary differential equation.