On the correspondence of hypercomplex solutions to special unitary groups

In the example of the nonlinear Klein–Gordon equation, we demonstrate that the even-indexed, hypergeometric solutions admit matrix representation that can be associated with special unitary groups. For the index 2, in particular, this correspondence is shown to be $1:1$. For the odd index 3, we show that no anticommuting matrices exist in the class of unitary anti-Hermitian matrices. We also show that in the electron-proton transport problem, the solution obtained describes the passage of the particles through the potential barrier.