Abstract
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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O. V. Kaptsov, Methods of Integrating Partial Differential Equations [in Russian], Fizmatlit, Moscow (2009).
O. V. Kaptsov, “On the problem of Goursats classification,” Programmirovanie, 2, 68–71 (2012).
M. E. Laine, “Sur l’application de la methode de Darboux aux equations s = f(x, y, z, p, q),” C. R. Acad. Sci. Paris, 182, 1126–1127 (1926).
A. V. Zhiber and V. V. Sokolov, “Exactly integrable hyperbolic equations of Liouville type,” Usp. Mat. Nauk, 56, No. 1 (337), 63–106 (2001).
A. V. Zhiber and A. M. Yurieva, “Hyperbolic Liouville type equations of a special class,” Itogi Nauki Tekh. Sovr. Mat. Prilozh. Temat. Obzory, 137, 17–25 (2017).
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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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DOI: https://doi.org/10.1007/s10958-020-05151-y