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Finite‐Dimensional Reductions and Finite‐Gap‐Type Solutions of Multicomponent Integrable PDEsстатья
Статья опубликована в высокорейтинговом журнале
Информация о цитировании статьи получена из
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 1 октября 2025 г.
- Авторы: Bolsinov Alexey V., Konyaev Andrey Yu, Matveev Vladimir S.
- Журнал: Studies in Applied Mathematics
- Том: 155
- Номер: 2
- Год издания: 2025
- Издательство: Blackwell Publishing Inc.
- Местоположение издательства: United Kingdom
- Номер статьи: e70100
- DOI: 10.1111/sapm.70100
- Аннотация: The main object of the paper is a recently discovered family of multicomponent integrable systems of partial differential equations, whose particular cases include many well-known equations such as the Korteweg–de Vries, coupled KdV, Harry Dym, coupled Harry Dym, Camassa–Holm, multicomponent Camassa–Holm, Dullin–Gottwald–Holm, and Kaup–Boussinesq equations. We suggest a methodology for constructing a series of solutions for all systems in the family. The crux of the approach lies in reducing this system to a dispersionless integrable system which is a special case of linearly degenerate quasilinear systems actively explored since the 1990s and recently studied in the framework of Nijenhuis geometry. These infinite-dimensional integrable systems are closely connected to certain explicit finite-dimensional integrable systems. We provide a link between solutions of our multicomponent PDE systems and solutions of this finite-dimensional system, and use it to construct animations of multicomponent analogous of soliton and cnoidal solutions.
- Добавил в систему: Коняев Андрей Юрьевич