Martínez Alonso, LuisMedina Reus, Elena2023-06-202023-06-202004-12-120305-447010.1088/0305-4470/37/50/005https://hdl.handle.net/20.500.14352/51652©IOP Publishing. The authors are grateful to Prof. Manuel Mañas for many useful discussions.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.engjournal articlehttp://dx.doi.org/10.1088/0305-4470/37/50/005http://iopscience.iop.orghttp://arxiv.org/abs/nlin/0409002open access51-73Boyer-Finley equationEinstein-Weyl spacesHodograph transformationIntegrable hierarchiesHeavenly equationGroup foliationKp hierarchyTau-functionSymmetriesLimitFísica-Modelos matemáticosFísica matemática