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首页> 外文期刊>Journal of physics, A. Mathematical and theoretical >Elliptic Euler-Poisson-Darboux equation, critical points and integrable systems
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Elliptic Euler-Poisson-Darboux equation, critical points and integrable systems

机译：椭圆Euler-Poisson-Darboux方程，临界点和可积系统

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摘要

The structure and properties of families of critical points for classes of functions W(z, z?) obeying the elliptic Euler-Poisson-Darboux equation E(1/2, 1/2) are studied. General variational and differential equations governing the dependence of critical points in variational (deformation) parameters are found. Explicit examples of the corresponding integrable quasi-linear differential systems and hierarchies are presented. There are the extended dispersionless Todaonlinear Schrodinger hierarchies, the inverse hierarchy and equations associated with the real-analytic Eisenstein series E(β, β?; 1/2) among them. The specific bi-Hamiltonian structure of these equations is also discussed.
机译：研究了服从椭圆型Euler-Poisson-Darboux方程E（1/2，1/2）的函数W（z，z？）的临界点族的结构和性质。找到控制临界点在变化（变形）参数中的依赖性的一般变化和微分方程。给出了相应的可积拟线性微分系统和层级的显式示例。其中有扩展的无色散度Toda /非线性Schrodinger层次结构，逆层次结构和与实解析爱森斯坦级数E（β，β?; 1/2）相关的方程。还讨论了这些方程式的特定双哈密顿结构。

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