Construction of scattering operators by the method of binary Darboux transformations
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 degenerat...
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| Дата: | 2006 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Українська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2006
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/3516 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | 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. |
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