关于Korteweg de Vries型方程的Bäcklund变换的分解
Decompositions of Bäcklund Transformations for the Korteweg-de Vries Equation
-
摘要: 本文讨论了Korteweg-de Vries(K-dV)方程,经修改的K-dV方程、高阶K-dV方程和柱面K-dV方程的scale变换和Bäcklund变换的分解,得出了Ba=Sa-1B1Sa型分解关系式.这对深入研究Bäcklund变换的内在结构,特别是对群结构性质极为有益的.Abstract: In this paper, decomposition relations such Ba=Sa-1B1Sa, connecting scale transformations and Bäcklund transformations for the Korteweg-de Vries K-dV, modified K-dV, higher-order K-dV and cylindrical equations, are obtained.
-
[1] Steudel,H.,Nother's theorem and higher conservation laws in ultrashort pulse propagation,Annalen der Physik,B32(1975),205-216. [2] Steudel,H.,Nother's theorem and the conservation laws of the Kortewegede Vries equation,ibid.,B32(1975),445-455. [3] Steudel,H.,Nonlinear Phenomena,A relation connecting scale transformation,Galilean transformation and Bäcklund transformation for the nonlinear Schr?dinger equation,Physica,D,1D(1980),420-421. [4] 屠规彰,Boussinesq方程的Backlund换与守恒律,应用数学学报,4.1(1981),63-68. [5] Boullough,R.K.and P.J.,Gaudrey,(ed.),Solitons,Topics in Current Physics,Vol.17,(Springer-Verlag,Berlin,Heidelberg,New York,(1980). [6] Hirota,R.,A new form of Bäcklund transformation and its relation to the inverse scattering problem,Prog.Phys.,52(1974),1498-1512. [7] Nimmo,J.J.C.and D.G.,Crighton,Bäcklund transformation for the cylindrical Korteweg-de Vries equation,Phys.Lett.82A(1981),211-214. [8] 黄迅成,自然杂志(研究通信),5,4(1982),313 [9] 黄迅成,科学通报,27,9(1982),569.
点击查看大图
计量
- 文章访问数: 1479
- HTML全文浏览量: 48
- PDF下载量: 520
- 被引次数: 0