Bäcklund Transformations and Darboux Integrability for Nonlinear Wave Equations

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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Published 1 January 2009