Noncommutative Boussinesq and NLS type 2- and 3-simplex maps

We construct noncommutative maps related to the Boussinesq and Nonlinear Schrödinger (NLS) equations with their variables belonging to a noncommutative division ring. We show that the noncommutative Boussinesq type map satisfies the Yang–Baxter equation, and it can be squeezed down to a noncommutative version of the Boussinesq lattice equation. Moreover, we show that the noncommutative NLS type map is a Zamolodchikov tetrahedron map.