Asian Journal of Mathematics

Volume 13 (2009)

Number 1

Bäcklund Transformations and Darboux Integrability for Nonlinear Wave Equations

Pages: 15 – 64

DOI: http://dx.doi.org/10.4310/AJM.2009.v13.n1.a3

Authors

Jeanne N. Clelland

Thomas A. Ivey

Abstract

We prove that second-order Monge-Ampère equations for one function of two variables are connected to the wave equation by a Bäcklund transformation if and only if they are integrable by the method of Darboux at second order.

Keywords

Bäcklund transformations; hyperbolic Monge-Ampère systems; exterior differential systems; Cartan's method of equivalence

2010 Mathematics Subject Classification

Primary 37K35, 58J72. Secondary 35L10, 53C10, 58A15.

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