Special Class of Liouville-Type Hyperbolic Equations
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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.
Keywordsx-integral y-integral Liouville-type equation differential substitution
AMS Subject Classification35Q51 37K60
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- 1.O. V. Kaptsov, Methods of Integration of Partial Differential Equations [in Russian], Fizmatlit, Moscow (2009).Google Scholar