HUANG Ding-jiang, ZHANG Hong-qing. Preliminary Group Classification of Quasi-Linear Third Order Evolution Equations[J]. Applied Mathematics and Mechanics, 2009, 30(3): 265-281.
Citation: HUANG Ding-jiang, ZHANG Hong-qing. Preliminary Group Classification of Quasi-Linear Third Order Evolution Equations[J]. Applied Mathematics and Mechanics, 2009, 30(3): 265-281.

Preliminary Group Classification of Quasi-Linear Third Order Evolution Equations

  • Received Date: 2008-06-24
  • Rev Recd Date: 2008-12-17
  • Publish Date: 2009-03-15
  • Group classification of quasilinear thir dorder evolution equations is performed by using the classical infinitesimal Lie method, the technique of equivalence transformations and the theory of classification of abstract low-dimensional Lie algebras. It is indicated that there are three equations admitting simple Lie algebras of dimension three. What's more, all the inequivalent equations admitting simple Lie algebra are nothing but them. Further more, it is also shown that there exist two, five, twenty-nine and twenty-six inequivalent third or der nonlinear evolution equations a dmitting one-, two, three, and fourdimensional solvable Lie algebras, respectively.
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