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.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 161, No. 2, pp. 176–190, November, 2009.
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Meshkov, A.G. Vector hyperbolic equations with higher symmetries. Theor Math Phys 161, 1471–1484 (2009). https://doi.org/10.1007/s11232-009-0134-z
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DOI: https://doi.org/10.1007/s11232-009-0134-z