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Preliminary group classification of quasilinear third-order evolution equations

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Abstract

Group classification of quasilinear third-order evolution equations is given by using the classical infinitesimal Lie method, the technique of equivalence transformations, and the theory of classification of abstract low-dimensional Lie algebras. We show that there are three equations admitting simple Lie algebras of dimension three. All non-equivalent equations admitting simple Lie algebras are nothing but these three. Furthermore, we also show that there exist two, five, twenty-nine and twenty-six nonequivalent third-order nonlinear evolution equations admitting one-, two-, three-, and four-dimensional solvable Lie algebras, respectively.

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Authors and Affiliations

  1. Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, P. R. China

    Ding-jiang Huang  (黄定江)

  2. Department of Applied Mathematics, Dalian University of Technology, Dalian, 116024, Liaoning Province, P. R. China

    Ding-jiang Huang  (黄定江) & Hong-qing Zhang  (张鸿庆)

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  1. Ding-jiang Huang  (黄定江)
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  2. Hong-qing Zhang  (张鸿庆)
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Correspondence to Hong-qing Zhang  (张鸿庆).

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(Contributed by Hong-qing ZHANG)

Project supported by the National Key Basic Research Project of China (973 Program) (No. 2004CB318000)

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Huang, Dj., Zhang, Hq. Preliminary group classification of quasilinear third-order evolution equations. Appl. Math. Mech.-Engl. Ed. 30, 275–292 (2009). https://doi.org/10.1007/s10483-009-0302-z

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  • DOI: https://doi.org/10.1007/s10483-009-0302-z

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

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