Special solutions for Ricci flow equation in 2D using the linearization approach

TL;DR

This paper explores special solutions to the 2D Ricci flow equation in conformal gauge by applying a linearization method, leading to new solutions involving arbitrary functions and various reductions.

Contribution

It introduces a linearization approach with a non-linear substitution to find new special solutions of the 2D Ricci flow equation, including arbitrary functions.

Findings

New special solutions involving arbitrary functions

Various reductions of the Ricci flow equation

Methodology for solving 2D Ricci flow equations

Abstract

The 2D Ricci flow equation in the conformal gauge is studied using the linearization approach. Using a non-linear substitution of logarithmic type, the emergent quadratic equation is split in various ways. New special solutions involving arbitrary functions are presented. Some special reductions are also discussed.