Symmetry Reduction of Exterior Differential Systems and Backlund Transformations for PDE in the Plane

TL;DR

This paper presents a method to construct Backlund transformations for Darboux integrable hyperbolic PDEs in the plane by using symmetry reduction of exterior differential systems, unifying previous results.

Contribution

It introduces a symmetry reduction approach to systematically derive Backlund transformations for a class of integrable PDEs, extending existing methods.

Findings

All Backlund transformations in arXiv:0707.4408v2 can be constructed via symmetry reduction.

The approach simplifies the derivation of transformations for Darboux integrable PDEs.

The method provides a unified framework for understanding Backlund transformations.

Abstract

We approach the construction of Backlund transformations for Darboux integrable hyperbolic partial differential equations in the plane through the reduction of exterior differential systems. For example it is shown that all the Backlund transformations in arXiv:0707.4408v2 can be constructed using symmetry reduction.