Analytical solutions to the cylindrically symmetric compressible isothermal Euler-Poisson equations of galaxies

In this paper, we study the cylindrically symmetric compressible isothermal Euler–Poisson equations of galaxies with a negative cosmological constant. By using some ansatzes, we construct a family of analytical periodic solutions to the system, which partially complements the result in Yuen (2009 Class. Quantum Grav. 26 235011), where a family of analytical periodic solutions to the system with spherical symmetry were given for the adiabatic exponent γ = 4 3 . Our result may provide an explanation about the dynamical evolution of the cylindrically symmetric galaxies or interstellar clouds.