Solutions of the Dispersionless Toda Hierarchy Constrained by String Equations

Abstract

Solutions of the Riemann-Hilbert problem implementing the twistorial structure of the dispersionless Toda (dToda) hierarchy are obtained. Two types of string equations are considered which characterize solutions arising in hodograph sectors and integrable structures of two-dimensional quantum gravity and Laplacian growth problems.

23 pages

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Cited by in corpus (4)

• Dispersionless bigraded Toda Hierarchy and its additional symmetry
• On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie
• Conformal Mappings and Dispersionless Toda hierarchy II: General String Equations
• Conformal Mappings and Dispersionless Toda hierarchy