Vector hyperbolic equations with higher symmetries
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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.
Keywordshyperbolic equation higher symmetry integral Bäcklund transformation exact integrability
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