Abstract
In the example of the nonlinear Klein-Gordon equation, we demonstrate that even-indexed hypergeometric solutions admit matrix representations that can be associated with special unitary groups. For the index 2 in particular, this correspondence is shown to be1 :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 the solutions obtained describe going around the potential barrier in the electron-proton transport problem.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 113, No. 1, pp. 29–33, October, 1997.
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Gudkov, V.V. On the relation between hypercomplex solutions and special unitary groups. Theor Math Phys 113, 1231–1234 (1997). https://doi.org/10.1007/BF02634010
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DOI: https://doi.org/10.1007/BF02634010