Seminar talk, 23 September 2026: Difference between revisions
Created page with "{{Talk | speaker = Oleg Morozov | title = A Lax representation, symmetries, and conservation laws for the three-dimensional Euler-Helmholtz equations | abstract = I will consider the three-dimensional Euler-Helmholtz equations for an inviscid incompressible fluid and reformulate them in a vorticity-type form by introducing a vector potential. I will exhibit a Lax representation with a non-removable parameter for the resulting system. I will discuss local symmetries and c..." |
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| title = A Lax representation, symmetries, and conservation laws for the three-dimensional Euler-Helmholtz equations | | title = A Lax representation, symmetries, and conservation laws for the three-dimensional Euler-Helmholtz equations | ||
| abstract = I will consider the three-dimensional Euler-Helmholtz equations for an inviscid incompressible fluid and reformulate them in a vorticity-type form by introducing a vector potential. I will exhibit a Lax representation with a non-removable parameter for the resulting system. I will discuss local symmetries and conservation laws of the system. Using the Lax representation, I will derive a shadow of a cosymmetry and find nonlocal conservation laws via the construction of the canonical conservation law on the Whitney sum of the tangent and cotangent coverings. Finally, I will present a Bäcklund transformation between the tangent and cotangent coverings and describe its action on local symmetries and local cosymmetries. | | abstract = I will consider the three-dimensional Euler-Helmholtz equations for an inviscid incompressible fluid and reformulate them in a vorticity-type form by introducing a vector potential. I will exhibit a Lax representation with a non-removable parameter for the resulting system. I will discuss local symmetries and conservation laws of the system. Using the Lax representation, I will derive a shadow of a cosymmetry and find nonlocal conservation laws via the construction of the canonical conservation law on the Whitney sum of the tangent and cotangent coverings. Finally, I will present a Bäcklund transformation between the tangent and cotangent coverings and describe its action on local symmetries and local cosymmetries. | ||
| video = | | video = https://video.gdeq.org/GDEq-zoom-seminar-20260923-Oleg_Morozov.mp4 | ||
| slides = | | slides = | ||
| references = {{arXiv|2409.05752}} | | references = {{arXiv|2409.05752}} | ||
| 79YY-MM-DD = 7973-90-76 | | 79YY-MM-DD = 7973-90-76 | ||
}} | }} | ||
Latest revision as of 22:27, 23 September 2026
Speaker: Oleg Morozov
Title: A Lax representation, symmetries, and conservation laws for the three-dimensional Euler-Helmholtz equations
Abstract:
I will consider the three-dimensional Euler-Helmholtz equations for an inviscid incompressible fluid and reformulate them in a vorticity-type form by introducing a vector potential. I will exhibit a Lax representation with a non-removable parameter for the resulting system. I will discuss local symmetries and conservation laws of the system. Using the Lax representation, I will derive a shadow of a cosymmetry and find nonlocal conservation laws via the construction of the canonical conservation law on the Whitney sum of the tangent and cotangent coverings. Finally, I will present a Bäcklund transformation between the tangent and cotangent coverings and describe its action on local symmetries and local cosymmetries.
Video
References:
arXiv:2409.05752