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arxiv: nlin/0612046 · v1 · submitted 2006-12-20 · 🌊 nlin.SI

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

L.V. Bogdanov , V.S. Dryuma , S.V. Manakov This is my paper
classification 🌊 nlin.SI
keywords equationdunajskihierarchydressingdunajskyformaccountanti-self-duality
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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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  1. Orlov-Schulman symmetries of the self-dual conformal structure equations

    nlin.SI 2026-04 unverdicted novelty 6.0

    Orlov-Schulman symmetries are constructed for the SDCS hierarchy with an explicit compatibility proof to Lax-Sato flows and a Riemann-Hilbert dressing scheme.