# The Unified Soliton System as the ${\rm AdS_2}$ System

## TL;DR

This paper explores a geometric framework that unifies various soliton equations, demonstrating that certain Einstein equations with constant scalar curvature encompass well-known integrable systems like KdV, mKdV, and sine-Gordon.

## Contribution

It introduces a Riemann geometric approach to unify soliton systems within a generalized Einstein equation framework.

## Key findings

- The Einstein equation with constant scalar curvature is integrable.
- Includes KdV, mKdV, and sine-Gordon equations as special cases.
- Provides a geometric perspective on soliton unification.

## Abstract

We study the Riemann geometric approach to be aimed at unifying soliton systems. The general two-dimensional Einstein equation with constant scalar curvature becomes an integrable differential equation. We show that such Einstein equation includes KdV/mKdV/sine-Gordon equations.