Seminar talk, 22 March 2017: Difference between revisions
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We illustrate our approach considering the dispersionless limit of the Kadomtsev-Petviashvili equation and the Mikhalev equation. | We illustrate our approach considering the dispersionless limit of the Kadomtsev-Petviashvili equation and the Mikhalev equation. | ||
Applications in three-dimensional case: | Applications in three-dimensional case:<br /> | ||
the theory of shock waves, the Whitham averaging approach. | the theory of shock waves, the Whitham averaging approach. | ||
| video = | | video = | ||
Latest revision as of 20:14, 15 March 2017
Speaker: Maxim Pavlov
Title: Multi-dimensional conservation laws and integrable systems
Abstract:
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.