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Rational Degenerations of M-Curves, Totally Positive Grassmannians and KP2-Solitonsстатья
Статья опубликована в высокорейтинговом журнале
Информация о цитировании статьи получена из
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Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 20 августа 2018 г.
- Авторы: Abenda Simonetta, Grinevich Petr G.
- Журнал: Communications in Mathematical Physics
- Том: 361
- Номер: 3
- Год издания: 2018
- Издательство: Springer Verlag
- Местоположение издательства: Germany
- Первая страница: 1029
- Последняя страница: 1081
- DOI: 10.1007/s00220-018-3123-y
- Аннотация: We establish a new connection between the theory of totally positive Grassmannians and the theory of 𝙼-curves using the finite-gap theory for solitons of the KP equation. Here and in the following KP equation denotes the Kadomtsev–Petviashvili 2 equation [see (1)], which is the first flow from the KP hierarchy. We also assume that all KP times are real. We associate to any point of the real totally positive Grassmannian Gr^{TP}(N,M) a reducible curve which is a rational degeneration of an 𝙼-curve of minimal genus g=N(M−N), and we reconstruct the real algebraic-geometric data á la Krichever for the underlying real bounded multiline KP soliton solutions. From this construction, it follows that these multiline solitons can be explicitly obtained by degenerating regular real finite-gap solutions corresponding to smooth 𝙼-curves. In our approach, we rule the addition of each new rational component to the spectral curve via an elementary Darboux transformation which corresponds to a section of a specific projection Gr^{TP}(r+1,M−N+r+1) to Gr^{TP}(r,M−N+r).
- Добавил в систему: Гриневич Петр Георгиевич