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Vector hyperbolic equations with higher symmetries. (English. Russian original) Zbl 1184.35016
Theor. Math. Phys. 161, No. 2, 1471-1484 (2009); translation from Teor. Mat. Fiz. 161, No. 2, 176-190 (2009).
Summary: 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.

MSC:
35B06 Symmetries, invariants, etc. in context of PDEs
35L76 Higher-order semilinear hyperbolic equations
58J70 Invariance and symmetry properties for PDEs on manifolds
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