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29 March 2024
 
  » arxiv » 1306.4192

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Elliptic Euler-Poisson-Darboux equation, critical points and integrable systems
B. G. Konopelchenko ; G. Ortenzi ;
Date 18 Jun 2013
AbstractStructure and properties of families of critical points for classes of functions $W(z,ar{z})$ 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 $E(eta,ar{{eta}};1/2)$among them. Specific bi-Hamiltonian structure of these equations is also discussed.
Source arXiv, 1306.4192
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