Geodesic
Symmetry Drivers and Formal Integrals of Hyperbolic Systems of Equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical physics, Tome 152 (2018), pp. 110-119

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In this paper, we consider symmetry drivers (i.e., operators that map arbitrary functions of one of independent variables into symmetries) and formal integrals (i.e., operators that map symmetries to the kernel of the total derivative). We prove that a hyperbolic system of partial differential equations has a complete set of formal integrals if and only if it admits a complete set of symmetry drivers. This assertion is also valid for difference and differential-difference analogs of scalar hyperbolic equations.
Keywords: nonlinear hyperbolic systems, Darboux integrability, higher symmetries, conservation laws and integrals
Mots-clés : Laplace invariants. 
@article{INTO_2018_152_a9,
     author = {S. Ya. Startsev},
     title = {Symmetry {Drivers} and {Formal} {Integrals} of {Hyperbolic} {Systems} of {Equations}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {110--119},
     publisher = {mathdoc},
     volume = {152},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_152_a9/}
}
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S. Ya. Startsev. Symmetry Drivers and Formal Integrals of Hyperbolic Systems of Equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical physics, Tome 152 (2018), pp. 110-119. http://geodesic.mathdoc.fr/item/INTO_2018_152_a9/