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arXiv · 1306.4192

Elliptic Euler-Poisson-Darboux equation, critical points and integrable systems

B. G. Konopelchenko·G. Ortenzi
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Abstract

Structure and properties of families of critical points for classes of functions $W(z,\bar{z})$ 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 Toda/nonlinear Schr\"{o}dinger hierarchies, the "inverse" hierarchy and equations associated with the real-analytic Eisenstein series $E(\beta,\bar{{\beta}};1/2)$among them. Specific bi-Hamiltonian structure of these equations is also discussed.

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B. G. Konopelchenko, G. Ortenzi. 2013-06-18. Elliptic Euler-Poisson-Darboux equation, critical points and integrable systems. https://doi.org/10.1088/1751-8113/46/48/485204

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