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1、Levi Painleve I . Painleve . Levi , : (1). (1+1) Levi , WTC Painleve , Painleve ( ) (1+1) Levi , Painleve Painleve , Painleve ( P- ). , , Schwarz . Backlund . (2). (2+1) Levi , WTC Painleve , (2+1) Levi , , . (3). Levi , , Matlab , . (2+1) Levi , . (4). (1+1) Levi , Painleve . : Painleve , , , Schwa
2、rz , 2006 II Abstract The integrable property for nonlinear differencial equations is important in nonlinear science. In this thesis, two higher order Levi equation are studied : (1). We make use of WTC method to the (1+1)-dimensional Levi equation. It is proved that the equation possess Painleve pr
3、operty (P-integrable). The resonances are obtained by the WTC method. The compatible equations are obtained and the expansions of solution are truncated through the analysis of compatibility. Thereby, the exact solutions and Daboux-Backlund Transformation of the Levi equation are obtained by means o
4、f Schwarzian derivative. (2). As to the (2+1)-dimensional Levi equation, we make use of WTC method to do the Painleve Test. Furthermore, One-soliton solution, Two-soliton solution, and N-soliton solution are obtained in some particular conditions. (3). We use Matlab to get graphics of Levi equation,
5、 and do some analysis about the solutions. Furthermore, the fission phenomenon in Two-soliton solution of the coupled (2+1)-dimensional Levi equation is discussed. (4). We introduce some special condition of the (1+1)-dimensional Levi equation in Painleve test, The compatible equations are obtained.
6、 Levi Painleve IIIKeywords: Painleve test, resonances, compatibility, Schwarzian derivative, solitary solution II . , , . . : : , . : : : : Levi Painleve 1 1.1 , . , , , , , , . , , , 1, 2, 3 . , , . 1965 N. J. Zabusky M. D. Kruskal (soliton, ) , . , : : , John scott Russell 4 , , . , . J. S. Russell , , , , , . 1895 , Amsterdam Korteweg , de Vries 5 , (KdV ), J. S. Russell . : 1955-1975 . 1955 , A. Fermi, J. Pasta, A. Ulam 6 , , : , . . FPU , N. J. Zabusky M. D. Kruskal 7 FPU , , , FPU , . 1965 , N. J. Zabusky M. D. Kruskal 8 KdV , ,
