Abstract
We construct integrable reductions of a soliton hierarchy associated with the special orthogonal Lie algebra so(3,R). The resulting reduced integrable equations include a nonlinear Schrödinger type equation and a modified Korteweg–de Vries type equation. There are two kinds of integrable reductions in our analysis, but they lead to essentially the same scalar integrable equations. This is a particular phenomenon for soliton equations associated with so(3,R), which is different from the one for soliton equations associated with sl(2,R).
•Scalar soliton hierarchies associated with so(3,R).•Innovative reductions, which keep the existence of infinitely many symmetries and conservation laws.•An integrable nonlinear Schrödinger type equation and an integrable modified Korteweg-de Vries type equation.