两分支Camassa-Holm系统Cauchy问题解的解析性

Analyticity of the Cauchy problem for a two-component Camassa-Holm system

利用抽象的Cauchy-Kowalevski定理,证明两分支Camassa-Holm系统Cauchy问题解的解析性,即系统的解关于空间变量是全局解析的,关于时间变量是局部解析的。该方法还可以用于讨论其他非线性偏微分方程解的解析性。

The abstract Cauchy-Kowalevski theorem is used to discuss the analyticity of the Cauchy problem for a two-component Camassa-Holm system.It is proved that its solutions are analytic in both variables,globally in space and locally in time.The same approach can be used to discuss the analyticity of the solutions for the other nonlinear partial differential equations.