论z_(xt)=0到φ_(xt)=G(φ)的Bcklund变换

Study of Bcklund Transformations from z_(xt)=0 to φ_(xt)=G(φ)

在波动方程zxt=0与二阶非线性偏微分方程φxt=G(φ)之间,若存在由某种可积系统定义的Bcklund变换z→φ,则可证明函数G只能是指数函数G(φ)=c1ec0φ(e=2.71828…,c0与c1为非零常量)的形式,相应的可积系统也同时被确定下来。

Between undulation equations zxt=0 and nonlinear second-order partial differential equations φxt=G （φ）, if there exist Backlund transformations z→φ defined by a certain integrable system, it can be proved that function G is the only form of index functions G （φ） =c1e^c0φ （e=2. 71828…, c0, c1 nonzero constants）. Meanwhile, the corresponding integrable systems can also be decided.