Integration of a nonlinear sine-Gordon–Liouville-type equation in the class of periodic infinite-gap functions
UDC 517.9 The method of inverse spectral problem  is used to integrate a nonlinear sine-Gordon–Liouville-type equation in the class of periodic infinite-gap functions. The evolution of the spectral data for the periodic Dirac operator  is introduced in which th...
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| Дата: | 2024 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2024
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/7610 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | UDC 517.9
The method of inverse spectral problem  is used to integrate a nonlinear sine-Gordon–Liouville-type equation in the class of periodic infinite-gap functions. The evolution of the spectral data for the periodic Dirac operator  is introduced in which the coefficient of the Dirac operator is a solution of a nonlinear sine-Gordon–Liouville-type  equation. The solvability of the Cauchy problemc is proved for an infinite system of Dubrovin differential equations in the class of three times continuously differentiable periodic infinite-gap functions. It is shown that the sum of a uniformly convergent functional series constructed by solving the system of Dubrovin differential equations and the first-trace formula satisfies the sine-Gordon–Liouville-type equation. |
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| DOI: | 10.3842/umzh.v76i8.7610 |