2026/2027
Интегрируемые системы частиц и нелинейные уравнения
Статус:
Дисциплина общефакультетского пула
Кто читает:
Факультет математики
Где читается:
Факультет математики
Когда читается:
3, 4 модуль
Охват аудитории:
для всех кампусов НИУ ВШЭ
Язык:
английский
Кредиты:
6
Контактные часы:
72
Course Syllabus
Abstract
The course is devoted to integrable systems of particles (such as Calogero-Moser and Ruijsenaars-Schneider and their spin generalizations) which are very interesting from mathematical point of view and find many applications in modern mathematical physics. They are closely connected with integrable nonlinear partial differential equations (soliton equations) through dynamics of poles of their singular solutions.
Course Contents
- Calogero – Moser systems: Hamiltonian, equations of motion, Lax representation, integrals of motion.
- Ruijsenaars – Schneider systems and their integrals of motion
- Deformed Ruijsenaars – Schneider systems.
- Spin generalizations of the Calogero – Moser and Ruijsenaars – Schneider systems
- The Kadomtsev – Petviashvili equation. The Calogero – Moser system as dynamics of poles of its elliptic solutions.
- 2D Toda chain and its elliptic solutions. The Ruijsenaars – Schneider system as dynamics of their poles
- Calogero – Moser and Ruijsenaars – Schneider systems in discrete time
