A quadratic completely integrated Burgers-type nonlinear model: conservation laws and Poisson structures - Kokovska, Ya.; Prytula, M. (Ukrains’kyi Matematychnyi Zhurnal, 2025)
UDC 517.9We study the complete integrability of a Burgers-type nonlinear quadratic dynamical system on a functional manifold. For this system, we prove the existence of an infinite hierarchy of functionally independent and involutive conservation laws and determine a compatible pair of Poisson operators, which allows us to rewrite the analyzed system in the bi-Hamiltonian form. We also construct a recursion operator generating an infinite hierarchy of commuting vector fields on a functional manifold.