摘要We discuss the motions of curves by introducing an extra spatial variable or equivalently, moving surfaces in affine geometries. It is shown that the 2+1-dimensional breaking soliton equation and a 2+1-dimensional nonlinear evolution equation regarded as a generalization to the 1+1-dimensional KdV equation arise from such motions.
Abstract：We discuss the motions of curves by introducing an extra spatial variable or equivalently, moving surfaces in affine geometries. It is shown that the 2+1-dimensional breaking soliton equation and a 2+1-dimensional nonlinear evolution equation regarded as a generalization to the 1+1-dimensional KdV equation arise from such motions.
LI Yan-Yan;QU Chang-Zheng;. Higher-Dimensional Integrable Systems Induced by Motions of Curves in Affine Geometries[J]. 中国物理快报, 2008, 25(6): 1931-1934.
LI Yan-Yan, QU Chang-Zheng,. Higher-Dimensional Integrable Systems Induced by Motions of Curves in Affine Geometries. Chin. Phys. Lett., 2008, 25(6): 1931-1934.
[1]Hasimoto H 1972 J. Fluid Mech. 51 477 [2]Lamb G L 1977 J. Math. Phys. 18 1654 [3]Langer J and Perline R 1991 J. Nonlinear Sci. 171 [4]Lakshmanan M 1979 J. Math. Phys. 20 1667 [5]Goldstein R E and Petrich D M 1991 Phys. Rev. Lett. 67 3203 [6]Nakayama K, Segur H and Wadati M 1992 Phys. Rev.Lett. 69 2603 [7]Chou K S and Qu C Z 2001 J. Phys. Soc. Jpn. 701912 [8]Chou K S and Qu C Z 2002 Physica D 162 9 [9]Chou K S and Qu C Z 2003 J. Nonlinear Sci. 13487 [10]Chou K S and Qu C Z 2002 Chaos, Solitons andFractals 14 29 [11]Wo W F and Qu C Z 2007 J. Geom. Phys. 57 1733 [12]Beffa G M, Sanders J A and Wang J P 2002 J. Nonlin.Sci. 12 143 [13]Beffa G M 2005 Proc. Am. Math. Soc. 134 779 [14]Ivey T A 2001 Contemp. Math. 285 71 [15]Anco S C 2006 J. Phys. A: Math. Gen. 392043 [16]Anco S C 2006 SIGMA 2(044) 1 [17]Myrzakulov R, Vijayalakshmi S, Nugmanova G N andLakshmanan M 1997 Phys. Lett. A 233 391 [18]Myrzakulov R, Vijayalakshmi S, Syzdykova R N andLakshmanan M 1998 J. Math. Phys. 39 2122 [19]Lakshmanan M, Myrzakulov R, Vijayalakshmi S and DanlybaevaA K 1998 J. Math. Phys. 39 3765 [20]Qu C Z and Zhang S L 2004 Chaos, Solitons andFractals 20 1013 [21]Nomizu K and Sasaki T 1994 Affine DifferentialGeometry (Cambridge: Cambridge University Press) [22]Calabi E, Olver P J and Tannenbaum A 1996 Adv.Math. 124 154
2008, Vol. 25 
