## Seminarium ZTOC## Część 1: Całkowalność uogólnionego równania typu Riemanna Część 2: O podstawach elektrodynamiki Makswella, warunku i sile Lorentza etc."## Anatolij K. Prykarpatski (AGH) |

Part 1: Short-wave perturbations in a relaxing medium, governed by a reduction of the Ostrovsky evolution equation (later derived by Whitham), are studied using the gradient-holonomic integrability algorithm. The bi-Hamiltonicity and complete integrability of the corresponding dynamical system is proved and an infinite hierarchy of commuting to each other conservation laws of dispersive type is constructed. The well defined regularization of the model is given and its Lax type integrability is demonstrated. A generalized hydrodynamic Riemann type system is also considered, infinite hierarchies of conservation laws, related compatible co-symplectic structures and Lax type representations are analyzed. Part 2: We are studying some new classical electrodynamics models of interacting charged point particles and the aspects of the quantization via the Dirac procedure. Based on the vacuum field theory no-geometry the Lagrangian and Hamiltonian reformulations of classical electrodynamics models are devised. The Dirac-type quantization procedure for the considered alternative electrodynamics models is discussed.