Martínez Alonso, LuisMedina Reus, Elena2023-06-202023-06-202004-12-12•[1] Takasaki K and Takebe T 1991 Lett. Math. Phys. 23 205 •[2] Takasaki K and Takebe T 1993 Lett. Math. Phys. 28 165 •[3] Takasaki K and Takebe T 1995 Rev. Math. Phys. 7 743 •[4] Dijkgraaf R, Moore G and Plesser R 1993 Nucl. Phys. B 394 356 •[5] Hanany A, Oz Y and Plesser M R 1994 Nucl. Phys. B 425 150 •[6] Takasaki K 1995 Commun. Math. Phys. 170 101 •[7] Wiegmann P W and Zabrodin P B 2000 Commun. Math. Phys. 213 523 •[8] Mineev-Weinstein M, Wiegmann P W and Zabrodin P B 2000 Phys. Rev. Lett. 84 5106 •[9] Boyer C P and Finley J D 1982 J. Math. Phys. 23 1126 •[10] Eguchi T, Gilkey P B and Hanson A J 1980 Phys. Rep. 66 213 •[11] Calderbank D M J and Tod K P 2001 Diff. Geom. Appl. 14 199 •[12] Jones P E and Tod K P 1985 Class. Quantum Grav. 2 565 •[13] Ward R S 1990 Class. Quantum Grav. 7 L95 •[14] Krichever I M 1992 Commun. Pure. Appl. Math. 47 437 •[15] Guil F, Mañas M and Martinez Alonso L 2003 J. Phys. A: Math. Gen. 36 4047 •[16] Mañas M and Martinez Alonso L 2004 Phys. Lett. A 320 383 •[17] Ferapontov E V, Korotkin D A and Shramchenko V A 2002 Class. Quantum Grav. 19 L205 •[18] Martina L, Sheftel M B and Winternitz P 2001 J. Phys. A: Math. Gen. 34 9243 •[19] Sheftel M B 2003 Theor. Math. Phys. 137 1743 •[20] Takasaki K and Takebe T 1992 Int. J. Mod. Phys. A 7 ((Suppl 1)) 889 •[21] Guil F, Mañas M and Martinez Alonso L 2003 J. Phys. A: Math. Gen. 36 6457 •[22] Martinez Alonso L and Mañas M 2003 J. Math. Phys. 44 3294 •[23] Teodorescu R, Bettelheim E, Agam O, Zabrodin A and Wiegmann P 2004 Normal random matrix ensemble as a growth problem Preprint hep-th/04011650305-447010.1088/0305-4470/37/50/005https://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