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On the dressing method for Dunajski anti-self-duality equation

L. V. Bogdanov·V. S. Dryuma·S. V. Manakov
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Abstract

A dressing scheme applicable to Dunajski equation is developed. Simple example of constructing solutions in terms of implicit functions is considered. Dunajski equation hierarchy is described, its Lax-Sato form is presented. Dunajsky equation hierarchy is characterised by conservation of three-dimensional volume form, in which a spectral variable is taken into account. Some reductions of Dunajsky equation hierarchy, including waterbag-type reduction, are studied.

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L. V. Bogdanov, V. S. Dryuma, S. V. Manakov. 2006-12-20. On the dressing method for Dunajski anti-self-duality equation. https://arxiv.org/abs/nlin/0612046

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