The Integration of Double-Infinite Toda Lattice by Means of Inverse Spectral Problem and Related Quetions
The solution of the Cauchy problem for differential-difference double-infinite Toda lattice by means of inverse spectral problem for semi-infinite block Jacobi matrix is given. Namely, we construct a simple linear system of three differential equations of first order whose solution gives the spectra...
Збережено в:
| Видавець: | Інститут математики НАН України |
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| Дата: | 2009 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2009
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| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/5711 |
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| Цитувати: | The integration of double-infinite Toda lattice by means of inverse spectral problem and related questions / Yu. Berezansky // Methods of Functional Analysis and Topology. — 2009. — Т. 15, № 2. — С. 101-136. — Бібліогр.: 48 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | The solution of the Cauchy problem for differential-difference double-infinite Toda lattice by means of inverse spectral problem for semi-infinite block Jacobi matrix is given. Namely, we construct a simple linear system of three differential equations of first order whose solution gives the spectral matrix measure of the aforementioned Jacobi matrix. The solution of the Cauchy problem for the Toda lattice is given by the procedure of orthogonalization w.r.t. this spectral measure, i.e. by the solution of the inverse spectral problem for this Jacobi matrix. |
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