Abelian subgroups of order automorphism group $({\rm Aut}(\mathbb R,\le), \circ )$

Question

I am searching for any results regarding Abelian subgroups of $({\rm Aut}(\mathbb R,\le), \circ )$, the order automorphism group of $\mathbb R$ (order automorphisms of $\mathbb R$ with the composition operation).

Are there any known results on the subject? Is there any book that covers the particular subject or any relevant monograph?