ABSTRACTIn this article, a general solution formula is derived for the ‐matrix modified Korteweg–de Vries equation. Then, a solution class corresponding to special parameter choices is examined in detail. Roughly, this class can be described as ‐solitons (in the sense of Goncharenko) with common phase matrix. It turns out that such a solution even takes values in a commutative subalgebra of the ‐matrices. We arrive at a rich picture of possibilities for generalized 1‐solitons and at visual patterns of ‐solitons which combine nonlinear with linear features. The impact of the phase matrix is visualized in computer plots.