Mutation of n-cotorsion pairs in triangulated categories

In this article, we define the notion of n-cotorsion pairs in triangulated categories, which is a generalization of the classical cotorsion pairs. We prove that any mutation of an n-cotorsion pair is again an n-cotorsion pair. When $n=1$, this result generalizes the work of Zhou and Zhu for classical cotorsion pairs. As applications, we give a geometric characterization of n-cotorsion pairs in n-cluster categories of type A and give a geometric realization of mutation of n-cotorsion pairs via rotation of certain configurations of n-diagonals.