2017
Том 69
№ 9

All Issues

Construction of scattering operators by the method of binary Darboux transformations

Pochynaiko M. D., Sidorenko Yu. M.

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Abstract

By using the binary Darboux transformations, we construct scattering operators for a Dirac system with special potential depending on 2n arbitrary functions of a single variable. It is shown that one of the operators coincides with the scattering operator obtained by Nyzhnyk in the case of degenerate scattering data. It is also demonstrated that the scattering operator for the Dirac system is either obtained as a composition of three Darboux self-transformations or factorized by two operators of binary transformations of special form. We also consider several cases of reduction of these operators.

English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 8, pp 1238-1260.

Citation Example: Pochynaiko M. D., Sidorenko Yu. M. Construction of scattering operators by the method of binary Darboux transformations // Ukr. Mat. Zh. - 2006. - 58, № 8. - pp. 1097–1115.

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