Parametric Bäcklund transformations I: Phenomenology

Clelland, Jeanne; Ivey, Thomas

doi:10.1090/S0002-9947-04-03536-6

Parametric Bäcklund transformations I: Phenomenology
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by Jeanne N. Clelland and Thomas A. Ivey PDF

Trans. Amer. Math. Soc. 357 (2005), 1061-1093 Request permission

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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