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Parametric Bäcklund transformations I: Phenomenology

Authors: Jeanne N. Clelland and Thomas A. Ivey
Journal: Trans. Amer. Math. Soc. 357 (2005), 1061-1093
MSC (2000): Primary 37K35, 58J72; Secondary 35L10, 53C10, 58A15
Published electronically: July 16, 2004
MathSciNet review: 2110433
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Abstract: We begin an exploration of parametric Bäcklund transformations for hyperbolic Monge-Ampère systems. (The appearance of an arbitrary parameter in the transformation is a feature of several well-known completely integrable PDEs.) We compute invariants for such transformations and explore the behavior of four examples, two of which are new, in terms of their invariants, symmetries, and conservation laws. We prove some preliminary results and indicate directions for further research.

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Additional Information

Jeanne N. Clelland
Affiliation: Department of Mathematics, 395 UCB, University of Colorado, Boulder, Colorado 80309-0395

Thomas A. Ivey
Affiliation: Department of Mathematics, College of Charleston, 66 George St., Charleston, South Carolina 29424-0001

Keywords: B\"acklund transformations, hyperbolic Monge-Amp\`ere systems, Weingarten surfaces, exterior differential systems, Cartan's method of equivalence
Received by editor(s): May 8, 2003
Received by editor(s) in revised form: September 4, 2003
Published electronically: July 16, 2004
Article copyright: © Copyright 2004 American Mathematical Society