# Sheftel M. Recursion operators and bi-Hamiltonian representations of cubic evolutionary (2+1)-dimensional systems (abstract)

Speaker: Mikhail Sheftel

Title: Recursion operators and bi-Hamiltonian representations of cubic evolutionary (2+1)-dimensional systems

Abstract:
We construct all (2+1)-dimensional PDEs which have the Euler-Lagrange form and determine the corresponding Lagrangians. We convert these equations and their Lagrangians to two-component forms and find Hamiltonian representations of all these systems using Dirac's theory of constraints. Integrability properties of one-parameter equations that are cubic in partial derivatives of the unknown are derived by our method of skew factorization of the symmetry condition. Lax pairs and recursion relations for symmetries are determined both for one-component and two-component form. For the integrable cubic one-parameter equations in the two-component form we obtain recursion operators in ${\displaystyle 2\times 2}$ matrix form and bi-Hamiltonian representations, thus discovering new bi-Hamiltonian (2+1) systems.

Slides: SheftelAMVconf2021slides.pdf

References:
arXiv:2109.04111

Event: Diffieties, Cohomological Physics, and Other Animals, 13-17 December 2021, Moscow.