Exact (1+1)-dimensional flows of a perfect fluid

TL;DR

This paper provides a comprehensive analytical solution to relativistic (1+1)-dimensional perfect fluid hydrodynamics, expressing the Khalatnikov potential through polynomial-based generating functions, enabling detailed flow reconstruction.

Contribution

It introduces a novel infinite-dimensional basis of solutions for relativistic (1+1)-dimensional perfect fluid flow using polynomial coefficients in the Khalatnikov potential.

Findings

Explicit general solution for relativistic (1+1)-dimensional flow

Representation of the Khalatnikov potential as polynomial combinations

Framework for reconstructing flow kinematics from the potential

Abstract

We present a general solution of relativistic (1+1)-dimensional hydrodynamics for a perfect fluid flowing along the longitudinal direction as a function of time, uniformly in transverse space. The Khalatnikov potential is expressed as a linear combination of two generating functions with polynomial coefficients of 2 variables. The polynomials, whose algebraic equations are solved, define an infinite-dimensional basis of solutions. The kinematics of the (1+1)-dimensional flow are reconstructed from the potential.