Conformal mappings and dispersionless Toda hierarchy. II: General string equations (Q982467)

The general evolutions of conformal mappings that can be described by dispersionless Toda hierarchies and derive the corresponding string equations are considered. The classification of solutions for a dispersionless Toda hierarchy into degenerate and non-degenerate cases was obtained. Every non-degenerate solutions is determined by a function \(H(z_1,z_2)\) of two variables. In this article was found explicit formulas for the tau function of dispersionless Toda hierarchies in terms \(H(z_1,z_2)\). For part I, cf. Commun. Math. Phys. 292, No. 2, 391--415 (2009; Zbl 1185.37150).