2005/04/29 by L. V. Bogdanov, B. G. Konopelchenko · 39 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Applied mathematics #Bilinear interpolation #Black Holes and Theoretical Physics #Geometry #Hamiltonian (control theory) #Hierarchy #Law #Mathematical analysis #Mathematical optimization #Mathematics #Nonlinear Waves and Solitons #Nonlinear system #Physics #Pure mathematics #Reduction (mathematics) #gr-qc #nlin.SI
paper · pdf · doi:10.1016/j.physleta.2005.07.002
published in Physics Letters A 345(1-3), 137-143 (Elsevier BV) · 11 pages
arxiv created 2005/04/29 · openalex publication_date 2005/07/13 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.