Murtazina, R. D. Nonlinear hyperbolic equations with characteristic ring of dimension 3. (Russian. English summary) Zbl 1249.35220 Ufim. Mat. Zh. 3, No. 4, 116-121 (2011). The paper provides a method of classification of Darboux integrable nonlinear hyperbolic equations \(u_{xy}=f(u,u_{x},u_{y})\) based on investigation of the characteristic pairs of Lie rings. Constructive conditions on the right-hand side \(f\) of the equation with characteristic ring of dimension three are obtained. These equations possess second-order integrals. In particular, a list of equations satisfying the constructive conditions is given for the equation \(u_{xy}=\varphi(u)\psi(u_{x})h(u_{y})\). Formulas for \(x\) - and \(y\)-integrals are given for these equations. Reviewer: Boris V. Loginov (Ul’yanovsk) Cited in 2 Documents MSC: 35L70 Second-order nonlinear hyperbolic equations 35B06 Symmetries, invariants, etc. in context of PDEs Keywords:Darboux integrable nonlinear hyperbolic equations of the second order; Lie characteristic ring; classification PDFBibTeX XMLCite \textit{R. D. Murtazina}, Ufim. Mat. Zh. 3, No. 4, 116--121 (2011; Zbl 1249.35220) Full Text: MNR