Parametric Bäcklund transformations I: Phenomenology |
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Authors: | Jeanne N Clelland Thomas A Ivey |
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Institution: | Department of Mathematics, 395 UCB, University of Colorado, Boulder, Colorado 80309-0395 ; Department of Mathematics, College of Charleston, 66 George St., Charleston, South Carolina 29424-0001 |
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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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Keywords: | B\"acklund transformations hyperbolic Monge-Amp\`ere systems Weingarten surfaces exterior differential systems Cartan's method of equivalence |
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