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

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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. 
@article{INTO_2018_152_a4,
     author = {A. V. Zhiber and A. M. Yur'eva},
     title = {On a {Certain} {Class} of {Hyperbolic} {Equations} with {Second-order} {Integrals}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {46--52},
     publisher = {mathdoc},
     volume = {152},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_152_a4/}
}
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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/