Seminar talk, 9 February 2022: Difference between revisions
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| title = Darboux integrability for diagonal systems of hydrodynamic type | | title = Darboux integrability for diagonal systems of hydrodynamic type | ||
| abstract = We prove that diagonal systems of hydrodynamic type are Darboux integrable if and only if the Laplace transformation sequences of the system for commuting flows terminate, give geometric interpretation for Darboux integrability of such systems in terms of congruences of lines and in terms of solution orbits with respect to symmetry subalgebras, show that Darboux integrable systems are necessarily semihamiltonian, and discuss known and new examples. | | abstract = We prove that diagonal systems of hydrodynamic type are Darboux integrable if and only if the Laplace transformation sequences of the system for commuting flows terminate, give geometric interpretation for Darboux integrability of such systems in terms of congruences of lines and in terms of solution orbits with respect to symmetry subalgebras, show that Darboux integrable systems are necessarily semihamiltonian, and discuss known and new examples. | ||
| video = https://video.gdeq. | | video = https://video.gdeq.org/GDEq-zoom-seminar-20220209-Sergey_Agafonov.mp4 | ||
| slides = | | slides = | ||
| references = | | references = | ||
| 79YY-MM-DD = 7977-97-90 | | 79YY-MM-DD = 7977-97-90 | ||
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Latest revision as of 08:40, 4 January 2025
Speaker: Sergey Agafonov
Title: Darboux integrability for diagonal systems of hydrodynamic type
Abstract:
We prove that diagonal systems of hydrodynamic type are Darboux integrable if and only if the Laplace transformation sequences of the system for commuting flows terminate, give geometric interpretation for Darboux integrability of such systems in terms of congruences of lines and in terms of solution orbits with respect to symmetry subalgebras, show that Darboux integrable systems are necessarily semihamiltonian, and discuss known and new examples.
Video