Ibragimov, N. H.; Torrisi, M.; Valenti, A. Preliminary group classification of equations \(v_{tt}=f(x,v_ x)v_{xx} +g(x,v_ x)\). (English) Zbl 0737.35099 J. Math. Phys. 32, No. 11, 2988-2995 (1991). Summary: A classification is given of equations \(v_{tt}=f(v,v_ x)v_{xx}+g(x,v_ x)\) admitting an extension by one of the principal Lie algebra of the equation under consideration. The paper is one of few applications of a new algebraic approach to the problem of group classification: the method of preliminary group classification. The result of the work is a wide class of equations summarized in Table II. Cited in 4 ReviewsCited in 66 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 58J70 Invariance and symmetry properties for PDEs on manifolds Keywords:symmetry groups; nonlinear telegraph equation; vibrating string; group classification of equations PDF BibTeX XML Cite \textit{N. H. Ibragimov} et al., J. Math. Phys. 32, No. 11, 2988--2995 (1991; Zbl 0737.35099) Full Text: DOI OpenURL References: [1] Lie S., Arch. Math. 6 pp 328– (1981) [2] Lie S., Arch. Math. 6 pp 112– (1981) [3] DOI: 10.1016/0020-7462(81)90018-4 · Zbl 0503.35058 [4] DOI: 10.1016/0020-7462(85)90007-1 · Zbl 0572.35070 [5] Torrisi M., Atti Sem. Mat. Fis. Univ. Modena pp 445– (1990) [6] Akhatov I. Sh., Mod. Probl. Math. 34 pp 3– (1989) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.