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Семинар отдела геометрии и топологии МИАН «Геометрия, топология и математическая физика» (семинар С. П. Новикова)
5 апреля 2017 г. 18:30, г. Москва, мехмат МГУ, ауд. 16-22
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Multi-Dimensional Conservation Laws and Integrable Systems
М. В. Павлов Физический институт им. П. Н. Лебедева РАН, г. Москва
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Количество просмотров: |
Эта страница: | 192 |
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Аннотация:
We introduce and investigate a new phenomenon in the Theory of Integrable Systems – the concept of multi-dimensional conservation laws for two- and three-dimensional integrable systems.
Existence of infinitely many local two-dimensional conservation laws is a well-known property of two-dimensional integrable systems.
We show that pairs of commuting two-dimensional integrable systems possess infinitely many three-dimensional conservation laws.
Examples: the Benney hydrodynamic chain, the Korteweg de Vries equation.
Simultaneously three-dimensional integrable systems (like the Kadomtsev-Petviashvili equation) have infinitely many three-dimensional quasi-local conservation laws.
We illustrate our approach considering the dispersionless limit of the Kadomtsev-Petviashvili equation and the Mikhalev equation.
Applications in three-dimensional case: the theory of shock waves, the Whitham averaging approach.
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