Solution classes of the matrix second Painlevé hierarchy

Abstract

We explore the generation of classes of solutions of the matrix second Painlevé hierarchy. This involves the consideration of the application of compositions of auto-Bäcklund transformations to different initial solutions, with the number of distinct solutions obtained for each value of the parameter appearing in the hierarchy depending on the symmetry properties of the chosen initial solution. This paper not only extends our previous results for the matrix second Painlevé equation itself, given in a recent paper, to the matrix second Painlevé hierarchy, but also provides a more detailed account of the underlying process.