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

2011/10/26 by Anderson, I. M., Fels, M. E.
#14E20 (Primary) 46E25 #20C20 (Secondary) #54C40 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1110.5777

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.

Related

• Backlund Transformations for Darboux Integrable Differential Systems
• Tangential symmetries of Darboux integrable systems
• Homogeneous Backlund transformations of hyperbolic Monge-Ampere systems
• Backlund Transformations and Darboux Integrability for Nonlinear Wave Equations
• Truncation-type methods and Backlund transformations for ordinary differential equations: the third and fifth Painleve equations