Geodesic
Characteristic algebras of nonlinear hyperbolic systems of equations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 3 (2010) no. 2, pp. 173-184

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We describe all $n$-component systems of nonlinear hyperbolic equations with a complete set of integrals of the first order and two-component systems of equations with three integrals of the first order and one integral of the second order. Necessary conditions for the existence of two integrals of the first order and two integral of second order for two-component systems of equations are obtained.
Keywords: characteristic algebra, integral, vector field, Riemann tensor. 
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Anatoly V. Zhiber; Olga S. Kostrigina. Characteristic algebras of nonlinear hyperbolic systems of equations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 3 (2010) no. 2, pp. 173-184. http://geodesic.mathdoc.fr/item/JSFU_2010_3_2_a4/