In the study of quantum field theory, one may encounter S-matrix a lot. Recently, in the study of integrability, I encountered R-matrix formulation which I am not familiar with.

First of all, the S-matrix is a scattering matrix which comes from scattering processes.

In the context of quantum mechanics and quantum field theory, we often compute the S-matrix, and we use well-known formulas, i.e, the LSZ reduction formula

On Wikipedia, they describe a R-matrix, as related with the Yang-Baxter equation (governing equation for integrability), and they add some comments that it is related with resonance.

My questions are, then:

1.Can you give me a clear definition and a governing equation for a R-matrix?

2.How are S-matrix and R-matrix related to each other?

3.Why is the R-matrix important in integrability (Yang-Baxter equation)?