摘要
本文探讨Ｓ－Ｇ方程的解和Ｅ＾３中负曲率曲面之间的联系，由此引出一个二阶椭园非线性偏微分方程（文中（１８）式）的求解问题。
In this paper, We would try to generalize the known results on Soliton equations and psoude--sphericai surfaces due to R. Sasaki, and derive the following Proposition. Let the function φ （u, v）is a soluton of Sine--Gorden equation, if, for some function λ（u, v）, the non--linear partial elliptic differential equation of order2 fuu＋fvv＋2Cot2 φ[ φufu ＋ φvfv ] ＋ λ^2e^2f- 1 =0 ……………………（＊）have a solution f （u, v）, then,there exist a Surface S in Ea WhoseGauss Curvature K （u, v） =-e^2f（u,v）（0 and whose the spread--anges of the asymptotic net on S are equat to 2 φ）（u, v）. also, the surfaceS is of Constant Curvature iff λ （u, v） =const. We conclude from the proposition that, if the differential equation（＊） has a solutioia corresponding to λ（u, v）≠const, then the Surface Srelevanced to the solution φ（u, v） of Sine--G6rden equation is non-- trivially conformal to the Pseude--spherical surface.
出处
《漳州师院学报》
1995年第4期10-13,共4页
Journal of ZhangZhou Teachers College（Philosophy & Social Sciences)
