Multi-layer quasi-geostrophic problem, Part I: Symmetries, Hamiltonian structure and conservation laws

by Serhii Koval (Інститут математики НАН України)

Monday 2 Nov 2026, 16:00 → 17:00 Europe/Kiev

https://bbb.imath.kiev.ua/rooms/dep-evh-zz9-ua9/join (ONLINE)

We carry out an extended symmetry analysis of the multi-layer quasi-geostrophic problem, a model given by a system of an arbitrary number of coupled barotropic vorticity equations. The first part of the talk focuses on various symmetry properties of the model.

Using several original tricks based on the complexification of spatial variables and the embedding of the original system into a chain of superclasses, we rigorously compute the Lie symmetry algebra of the model. Subsequently, using the megaideal-based version of the algebraic method, we find the point symmetry pseudogroup of the system and classify its discrete elements. Using the vector representation of the model, we study its Hamiltonian structure, conservation laws and Hamiltonian symmetries.

Part II will be devoted to the Lie reductions of the multi-layer quasi-geostrophic problem and the construction of its exact invariant solutions.

This talk is based on the joint work with A. Bihlo and R. Popovych: 
Symmetry analysis and exact solutions of multi-layer quasi-geostrophic problem, J. Nonlinear Sci. 36 (2026), 113, 82 pp, arXiv:2603.26959.