Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (3): 275-292.doi: https://doi.org/10.1007/s10483-009-0302-z
黄定江
Ding-Jiang HUANG
摘要: 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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