This article is cited in 2 papers

Vector hyperbolic equations with higher symmetries

A. G. Meshkov

Orel State University for Technology, Orel, Russia

Abstract: We list eleven vector hyperbolic equations that have third-order symmetries with respect to both characteristics. This list exhausts the equations with at least one symmetry of a divergence form. We integrate four equations in the list explicitly, bring one to a linear form, and bring four more to nonlinear ordinary nonautonomous systems. We find the Bäcklund transformations for six equations.

Keywords: hyperbolic equation, higher symmetry, integral, Bäcklund transformation, exact integrability.

Received: 30.04.2008
Revised: 15.04.2009

DOI: 10.4213/tmf6430

 English version: Theoretical and Mathematical Physics, 2009, 161:2, 1471–1484

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