Geodesic
On a Certain Class of Hyperbolic Equations with Second-order Integrals
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical physics, Tome 152 (2018), pp. 46-52.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we examine a special class of nonlinear hyperbolic equations possessing a second-order $y$-integral. We clarify the structure of $x$-integrals and prove that they are $x$-integrals of a hyperbolic equation with a first-order $y$-integral. We also prove that this class contains the well-known Laine equation.
Mots-clés : Liouville-type equations
Keywords: differential substitutions, $x$- and $y$-integrals. 
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A. V. Zhiber; A. M. Yur'eva. On a Certain Class of Hyperbolic Equations with Second-order Integrals. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical physics, Tome 152 (2018), pp. 46-52. http://geodesic.mathdoc.fr/item/INTO_2018_152_a4/

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