The Generalized Marchenko Method in the Inverse Scattering Problem for a First-Order Linear System with Energy-Dependent Potentials
The Marchenko method is developed in the inverse scattering problem for a linear system of first-order differential equations containing potentials proportional to the spectral parameter. The corresponding Marchenko system of integral equations is derived in such a way that the method can be applied...
Збережено в:
| Дата: | 2023 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2023
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| Теми: | |
| Онлайн доступ: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/995 |
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| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
Репозитарії
Journal of Mathematical Physics, Analysis, Geometry| Резюме: | The Marchenko method is developed in the inverse scattering problem for a linear system of first-order differential equations containing potentials proportional to the spectral parameter. The corresponding Marchenko system of integral equations is derived in such a way that the method can be applied to some other linear systems for which a Marchenko method is not yet available. It is shown how the potentials and the Jost solutions to the linear system are constructed from the solution to the Marchenko system. The bound-state information for the linear system with any number of bound states and any multiplicities is described in terms of a pair of constant matrix triplets. When the potentials in the linear system are reflectionless, some explicit solution formulas are presented in closed form for the potentials and for the Jost solutions to the linear system. The theory is illustrated with some explicit examples.
Mathematical Subject Classification 2020: 34A55, 34L25, 34L40, 47A40 |
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