Geodesic
Vector hyperbolic equations with higher symmetries
Teoretičeskaâ i matematičeskaâ fizika, Tome 161 (2009) no. 2, pp. 176-190

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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.
Keywords: hyperbolic equation, higher symmetry, integral, Bäcklund transformation, exact integrability. 
@article{TMF_2009_161_2_a3,
     author = {A. G. Meshkov},
     title = {Vector hyperbolic equations with higher symmetries},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {176--190},
     publisher = {mathdoc},
     volume = {161},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_161_2_a3/}
}
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A. G. Meshkov. Vector hyperbolic equations with higher symmetries. Teoretičeskaâ i matematičeskaâ fizika, Tome 161 (2009) no. 2, pp. 176-190. http://geodesic.mathdoc.fr/item/TMF_2009_161_2_a3/