Analytical solutions of Landau (1+1)-dimensional hydrodynamics

To help guide our intuition, summarize important features, and point out essential elements, we review the analytical solutions of Landau (1+1)-dimensional hydrodynamics and discuss the full evolution of the dynamics from the very beginning. Special emphasis is placed on the matching and the interplay between the Khalatnikov solution and the Riemann simple wave solution, at the earliest times and in the edge regions at later times. These analytical solutions collected and developed here serve well as a useful guide and cross-check in the development of complicated numerically intensive relativistic hydrodynamical Monte Carlo simulations.