N-Soliton matrix mKdV solutions: some special solutions revisited

In this article, a general solution formula is derived for the (Formula presented.) -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 (Formula presented.) -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 (Formula presented.) -matrices. We arrive at a rich picture of possibilities for generalized 1-solitons and at visual patterns of (Formula presented.) -solitons which combine nonlinear with linear features. The impact of the phase matrix is visualized in computer plots.