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Nonlinear Beltrami equation and tau-function for dispersionless hierarchies

L. V. Bogdanov·B. G. Konopelchenko
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Abstract

It is proved that the action for nonlinear Beltrami equation (quasiclassical dbar-problem) evaluated on its solution gives a tau-function for dispersionless KP hierarchy. Infinitesimal transformations of tau-function corresponding to variations of dbar-data are found. Determinant equations for the function generating these transformations are derived. They represent a dispersionless analogue of singular manifold (Schwarzian) KP equations. Dispersionless 2DTL hierarchy is also considered.

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L. V. Bogdanov, B. G. Konopelchenko. 2003-10-27. Nonlinear Beltrami equation and tau-function for dispersionless hierarchies. https://doi.org/10.1016/j.physleta.2004.01.033

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