Geodesic
Special class of of Liouville-type hyperbolic equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical physics, Tome 137 (2017), pp. 17-25.

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In this paper, we obtain differential substitutions for a special class of Liouville-type equations that simplify these equations. We present necessary and sufficient conditions of the existence of $y$-integrals of the second order. We examine the principal case of necessary and sufficient conditions of the existence of $y$-integrals.
Keywords: $x$-integral, $y$-integral, differential substitution.
Mots-clés : Liouville-type equation 
@article{INTO_2017_137_a1,
     author = {A. V. Zhiber and A. M. Yur'eva},
     title = {Special class of of {Liouville-type} hyperbolic equations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {17--25},
     publisher = {mathdoc},
     volume = {137},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_137_a1/}
}
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A. V. Zhiber; A. M. Yur'eva. Special class of of Liouville-type hyperbolic equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical physics, Tome 137 (2017), pp. 17-25. http://geodesic.mathdoc.fr/item/INTO_2017_137_a1/