Integrable hierarchy for multidimensional Toda equations and topological–anti-topological fusion

2001/07/31 by H. Aratyn, J. F. Gomes, A. H. Zímerman +1 · 26 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics #Hierarchy #Integrable system #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Topological quantum number #Topological space #Topology (electrical circuits) #hep-th #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1016/s0393-0440(02)00126-2

published in Journal of Geometry and Physics 46(1), 21-47 (Elsevier BV) · 24+1 pages, some minus signs corrected

arxiv created 2001/09/26 · openalex publication_date 2003/02/17 · arxiv updated 2014/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The negative symmetry flows are incorporated into the Riemann-Hilbert problem for the homogeneous A_m-hierarchy and its gl (m+1, C) extension. A loop group automorphism of order two is used to define a sub-hierarchy of gl (m+1, C) hierarchy containing only the odd symmetry flows. The positive and negative flows of the ± 1 grade coincide with equations of the multidimensional Toda model and of topological-anti-topological fusion.

Citations

• Differential Geometry, Lie Groups, and Symmetric Spaces
• On Grassmannian description of the constrained KP hierarchy
• Ising model andN=2 supersymmetric theories
• Affine Lie algebraic origin of constrained KP hierarchies

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• New soliton solutions for Chen-Lee-Liu and Burgers hierarchies and its Bäcklund transformations