Applications of Nijenhuis geometry IV: multicomponent KdV and Camassa-Holm equations

We construct a new series of multi-component integrable PDE systems that contains as particular examples (with appropriately chosen param-eters) and generalises many famous integrable systems including KdV, coupled KdV [1], Harry Dym, coupled Harry Dym [2], Camassa-Holm, multi-component Camassa-Holm [14], Dullin-Gottwald-Holm and Kaup-Boussinesq systems. The series also contains integrable systems with no low-component analogues.