The Unified Soliton System as the $\mathrm{Ad}{\mathrm{S}}_2$ System

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.

8 pages

References in corpus (3)

• Lie and Noether point Symmetries for a Class of Nonautonomous Dynamical Systems
• The Static Elliptic $N$-soliton Solutions of the KdV Equation
• The Construction of the mKdV Cyclic Symmetric $N$-soliton Solution by the Bäcklund Transformation

Cited by in corpus (2)

• Common Hirota Form Bäcklund Transformation for the Unified Soliton System
• Elliptic Solutions for Higher Order KdV Equations