Integrable Hierarchy for Multidimensional Toda Equations and Topological-Anti-topological Fusion

Abstract

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

24+1 pages, some minus signs corrected

References in corpus (1)

• The complex Sine-Gordon equation as a symmetry flow of the AKNS Hierarchy

Cited by in corpus (23)

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• Soliton Solutions for the Super mKdV and sinh-Gordon Hierarchy
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• Negative flows of generalized KdV and mKdV hierarchies and their gauge-Miura transformations
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• A Class of Mixed Integrable Models
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• Non Abelian Toda models and Constrained KP hierarchies
• Clifford Algebra Derivations of Tau-Functions for Two-Dimensional Integrable Models with Positive and Negative Flows
• Integrable Structure behind WDVV Equations
• WDVV Equations, Darboux-Egoroff Metric and the Dressing Method
• Supersymmetry of Affine Toda Models as Fermionic Symmetry Flows of the Extended mKdV Hierarchy
• String Equations of the q-KP Hierarchy
• SKdV, SmKdV flows and their supersymmetric gauge-Miura transformations
• Generalized Riemann-Hilbert-Birkhoff Decomposition and a New Class of Higher Grading Integrable Hierarchies
• Additional symmetry of the modified extended Toda hierarchy
• New soliton solutions for Chen-Lee-Liu and Burgers hierarchies and its Bäcklund transformations
• New negative grade solitonic sector for supersymmetric KdV and mKdV hierarchies