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| 1 | Maximal Dimension of Invariant Subspaces to Systems of Nonlinear Evolution Equations显示文摘In this paper,the dimension of invariant subspaces admitted by nonlinear systems is estimated under certain conditions.It is shown that if the two-component nonlinear vector differential operator F=(F 1,F 2) with orders {k 1,k 2 } (k 1 ≥ k 2) preserves the invariant subspace W 1 n 1 × W 2 n 2 (n 1 ≥ n 2),then n 1 n 2 ≤ k 2,n 1 ≤ 2(k 1 + k 2) + 1,where W q n q is the space generated by solutions of a linear ordinary differential equation of order n q (q=1,2).Several examples including the (1+1)-dimensional diffusion system and Ito 's type,Drinfel'd-Sokolov-Wilson's type and Whitham-Broer-Kaup's type equations are presented to illustrate the result.Furthermore,the estimate of dimension for m-component nonlinear systems is also given. | Shoufeng SHEN Changzheng QU Yongyang JIN Lina JI | 2012 | Chinese Annals of Mathematics,Series B2012，33，2： | 13 |
| 2 | Lie group classification of the N-th-order nonlinear evolution equations显示文摘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. | SHEN ShouFeng QU ChangZheng HUANG Qing JIN YongYang | 2011 | Science China Mathematics2011，54，12： | 1 |
| 3 | New exact solutions of the (2 + 1)-dimensional KdV equation with variable coefficients显示文摘 | Shen Shoufeng Zhang Jun Ye Cai' er | 2005 | Phy Lett A2005，337，： | 1 |
| 4 | NEW PERIODIC SOLUTIONS OF NONLINEAR EVOLUTION EQUATIONS显示文摘In this paper,some new periodic solutions of nonlinear evolution equations and corresponding travelling wave solutions are obtained by using the double function method and Jacobi elliptic functions. | Shen Shoufeng Pan ZuliangDept.of Math.,Zhejiang Univ.,Hangzhou 310027,China | 2002 | Applied Mathematics(A Journal of Chinese Universities)2002，17，4： | 0 |
| 5 | LIE SYMMETRY ANALYSIS AND PAINLEVE ANALYSIS OF THE NEW(2+l)-DIMENSIONAL KdV EQUATION显示文摘与联系的谎言点对称新(2+1 ) 维的 KdV equationu_t + 3u_xu_y +u_(xxy )= 0 被调查。一些类似减小被解决相应特战程导出。为这个方程的 Painleve 分析也被介绍,孤立子答案从 Baecklund 转变直接被获得。 | Shen Shoufeng | 2007 | Applied Mathematics(A Journal of Chinese Universities)2007，22，2： | 0 |
| 6 | Lie symmetry analysis, optimal system and conservation laws of a new(2+1)-dimensional KdV system显示文摘In this paper, Lie point symmetries of a new(2+1)-dimensional KdV system are constructed by using the symbolic computation software Maple. Then, the one-dimensional optimal system,associated with corresponding Lie algebra, is obtained. Moreover, the reduction equations and some explicit solutions based on the optimal system are presented. Finally, the nonlinear selfadjointness is provided and conservation laws of this KdV system are constructed. | Mengmeng Wang Shoufeng Shen Lizhen Wang | 2021 | Communications in Theoretical Physics2021，73，8： | 0 |
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