摘要
In this paper, Lie group classification to the N-th-order nonlinear evolution equation Ut ： UNx ＋ F（x, t, u, ux, . . . , U（N-1）x）is performed. It is shown that there are three, nine, forty-four and sixty-one inequivalent equations admitting one-, two-, three- and four-dimensionM solvable Lie algebras, respectively. We also prove that there are no semisimple Lie group 50（3） as the symmetry group of the equation, and only two realizations oral（2, R） are admitted by the equation. The resulting invariant equations contain both the well-known equations and a variety of new ones.
In this paper, Lie group classification to the N-th-order nonlinear evolution equation ut=uNx + F(x1t1u1ux1, . . . 1u(N-1)x) is performed. It is shown that there are three, nine, forty-four and sixty-one inequivalent equations admitting one-, two-, three- and four-dimensional solvable Lie algebras, respectively. We also prove that there are no semisimple Lie group so(3) as the symmetry group of the equation, and only two realizations of sl(2, R) are admitted by the equation. The resulting invariant equations contain both the well-known equations and a variety of new ones.
基金
supported by National Natural Science Foundation of China (Grant Nos.11001240, 10926082)
the Natural Science Foundation of Zhejiang Province (Grant Nos. Y6090359, Y6090383)
the National Natural Science Foundation for Distinguished Young Scholars of China (Grant No. 10925104)
the Natural Science Foundation of Shaanxi Province (Grant No. 2009JQ1003)
