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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Geometry of Bäcklund transformations I: generality


Author: Yuhao Hu
Journal: Trans. Amer. Math. Soc. 373 (2020), 1181-1210
MSC (2010): Primary 37K35, 35L10, 58A15, 53C10
DOI: https://doi.org/10.1090/tran/7992
Published electronically: November 5, 2019
MathSciNet review: 4068261
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Abstract: Using Élie Cartan’s method of equivalence, we prove an upper bound for the generality of generic rank-1 Bäcklund transformations relating two hyperbolic Monge-Ampère systems. In cases when the Bäcklund transformation admits a symmetry group whose orbits have codimension 1, 2, or 3, we obtain classification results and new examples of auto-Bäcklund transformations.


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Additional Information

Yuhao Hu
Affiliation: Department of Mathematics, 395 UCB, University of Colorado, Boulder, Colorado 80309-0395
Email: Yuhao.Hu@colorado.edu

Keywords: Bäcklund transformations, hyperbolic Monge-Ampère systems, exterior differential systems, Cartan’s method of equivalence.
Received by editor(s): February 26, 2019
Received by editor(s) in revised form: June 25, 2019
Published electronically: November 5, 2019
Article copyright: © Copyright 2019 American Mathematical Society