Martínez Alonso, LuisMedina Reus, Elena2023-06-202023-06-202008-08-221751-811310.1088/1751-8113/41/33/335202https://hdl.handle.net/20.500.14352/51635©IOP Publishing Ltd. The authors wish to thank the Spanish Ministerio de Educación y Ciencia (research project FIS2005-00319) and the European Science Foundation (MISGAM programme) for their support.Critical points of semiclassical expansions of solutions to the dispersionful Toda hierarchy are considered and a double scaling limit method of regularization is formulated. The analogues of the critical points characterized by the strong conditions in the Hermitian matrix model are analysed and the property of doubling of equations is proved. A wide family of sets of critical points is introduced and the corresponding double scaling limit expansions are discussed.engjournal articlehttp://dx.doi.org/10.1088/1751-8113/41/33/335202http://iopscience.iop.orghttp://arxiv.org/abs/0804.3498open access51-73Matrix modelsIntegrable hierarchiesQuantum-gravityUniversalityEquationsStrings1stFísica-Modelos matemáticosFísica matemática