On a Certain Class of Hyperbolic Equations with Second-Order Integrals


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.

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Correspondence to A. V. Zhiber.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 152, Mathematical Physics, 2018.

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Zhiber, A.V., Yur’eva, A.M. On a Certain Class of Hyperbolic Equations with Second-Order Integrals. J Math Sci 252, 168–174 (2021). https://doi.org/10.1007/s10958-020-05151-y

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Keywords and phrases

  • Liouville-type equations
  • differential substitutions
  • x- and y-integrals

AMS Subject Classification

  • 35Q51
  • 37K60