Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Prof. Pilar Ruiz Gordoa,Universidad Rey Juan Carlos, Madrid, Spain
Inviter:
Title:
Second and fourth matrix Painleve hierarchies
Time & Venue:
2019.4.19 20:00-21:00 N702
Abstract:
In this talk we consider the construction of hierarchies of matrix ordinary differential equations, analogous to scalar Painlev ?e hierarchies. By considering generalized matrix KdV and mKdV hierarchies we derive a matrix first Painlev ?e hierarchy and a matrix second Painlev ?e hierarchy. The relationship between the matrix mKdV equation and the matrix second Painlev ?e equation is thus clarified. We also investigate properties of the matrix second Painlev ?e hierarchy, e.g., auto-B ?acklund transformations. We consider further examples of matrix Painlev ?e equations. Our work shows how properties of matrix ODEs can be derived using structures of related matrix PDEs.