Nonlinear Evolution of Disturbances in a (1+1)-Dimensional Universe

TL;DR

This paper derives an exact analytical solution for the nonlinear evolution of arbitrary disturbances in a (1+1)-dimensional universe, providing a valuable test case for numerical methods and illustrating the nonlinear distortion of sinusoidal density perturbations.

Contribution

It presents the first exact solution for nonlinear disturbance evolution in a (1+1)-dimensional universe, useful for testing numerical simulations.

Findings

Exact solution for nonlinear disturbance evolution

Illustration of nonlinear distortion of sinusoidal perturbations

Provides a benchmark for numerical methods

Abstract

General exact solution is obtained for the problem of the development of arbitrary disturbances of the density and velocity in a (1+1)-dimensional universe. This analytical solution may serve, particularly, as a test for numerical methods. For an illustration, the nonlinear distortion of a sinusoidal perturbation of the initial density is calculated.