Preliminary group classification of equations \(v_{tt}=f(x,v_ x)v_{xx} +g(x,v_ x)\). (English) Zbl 0737.35099

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.


35Q53 KdV equations (Korteweg-de Vries equations)
58J70 Invariance and symmetry properties for PDEs on manifolds
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[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)
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