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Article overview
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Elliptic Euler-Poisson-Darboux equation, critical points and integrable systems | B. G. Konopelchenko
; G. Ortenzi
; | Date: |
18 Jun 2013 | Abstract: | Structure 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 | Services: | Forum | Review | PDF | Favorites |
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