Dunajski generalization of the second heavenly equation: dressing method and the hierarchy

2007/07/11 by L. V. Bogdanov, L V Bogdanov, V. S. Dryuma +3 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Analytic and geometric function theory #Nonlinear Waves and Solitons #nlin.SI

paper · pdf · doi:10.1088/1751-8113/40/48/005

published as Journal of Physics A, 40 (2007) 14383-14393 · 13 pages

arxiv created 2007/07/11 · openalex publication_date 2007/11/14 · arxiv updated 2010/11/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31

Abstract

Dunajski generalization of the second heavenly equation is studied. A dressing scheme applicable to the Dunajski equation is developed; an example of constructing solutions in terms of implicit functions is considered. A Dunajski equation hierarchy is described, and its Lax–Sato form is presented. The Dunajski equation hierarchy is characterized by the conservation of a three-dimensional volume form, in which a spectral variable is taken into account.

Citations

• Inverse scattering problem for vector fields and the Cauchy problem for the heavenly equation
• On the heavenly equation hierarchy and its reductions

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