On the dbar-dressing method applicable to heavenly equation

L. V. Bogdanov; B. G. Konopelchenko

doi:10.1016/j.physleta.2005.07.002

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On the dbar-dressing method applicable to heavenly equation

L. V. Bogdanov·B. G. Konopelchenko

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Abstract

The $\dbar$-dressing scheme based on local nonlinear vector $\dbar$-problem is developed. It is applicable to multidimensional nonlinear equations for vector fields, and, after Hamiltonian reduction, to heavenly equation. Hamiltonian reduction is described explicitely in terms of the $\dbar$-data. An analogue of Hirota bilinear identity for heavenly equation hierarchy is introduced, $τ$-function for the hierarchy is defined. Addition formulae (generating equations) for the $τ$-function are found. It is demonstrated that $τ$-function for heavenly equation hierarchy is given by the action for $\dbar$-problem evaluated on the solution of this problem.

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L. V. Bogdanov, B. G. Konopelchenko. 2005-04-29. On the dbar-dressing method applicable to heavenly equation. https://doi.org/10.1016/j.physleta.2005.07.002

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