Ariznabarreta García de Cortázar, GerardoMañas Baena, Manuel Enrique2023-06-222023-06-222022-02-250167-278910.1016/j.physd.2022.133202https://hdl.handle.net/20.500.14352/71532CRUE-CSIC (Acuerdos Transformativos 2022). © 2022 The Author(s). Thanks financial support from the Universidad Complutense de Madrid Program ‘‘Ayudas para Becas y Contratos Complutenses Predoctorales en España 2011’’. Thanks financial support from the Spanish ‘‘Agencia Estatal de Investigación’’ research project [PGC2018-096504-B-C33] , Ortogonalidad y Aproximación: Teoría y Aplicaciones en Física MatemáticaA new multivariate Toda hierarchy of nonlinear partial differential equations adapted to multivariate biorthogonal polynomials is discussed. This integrable hierarchy is associated with non-standard multivariate biorthogonality. Wave and Baker functions, linear equations, Lax and Zakharov–Shabat equations, KP type equations, appropriate reductions, Darboux or linear spectral transformations, and bilinear equations involving linear spectral transformations are presented.engAtribución 3.0 Españahttps://creativecommons.org/licenses/by/3.0/es/journal articlehttps://doi.org/10.1016/j.physd.2022.133202https://www.sciencedirect.comopen access51-73Multivariate orthogonal polynomialsMultivariate Toda hierarchyGeneralized KP equationsBilinear equationsBorel–Gauss factorizationQuasi-determinantsFísica-Modelos matemáticosFísica matemática