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Information × Registration Number 0221U102575, 0116U005037 , R & D reports Title Classical and quantum transformation groups, inverse problems and non-linear integrable equations popup.stage_title Head Kotlyarov Volodymyr P, Доктор технічних наук Registration Date 05-02-2021 Organization B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine popup.description2  Objects of research are initial-boundary value problems for nonlinear integrable equations, inverse problems for Lax equations and spectral theory of perturbed operators, the Baker-Akhiezer functions, approximate solutions of the Boltzmann equation, Laurent extensions of the quantum plane and quantum disk, infinite groups. The purpose of the work is to develop methods for solving and asymptotic research of nonlinear problems for integrable equations; inverse problems for perturbed operators; approximation of solutions of the Boltzmann equation; problems of the theory of quantum groups and images of an infinite symmetric group with conditions of stability and invariance. Research methods are developed and generalized: finite-zone integration method; the method of the inverse problem in the form of the Riemann-Hilbert problem for step-like initial data; methods of the Riemann-Hilbert problem for initial-boundary value problems for integrable nonlinear equations; asymptotic methods for initial-boundary value problems for nonlinear equations; methods of group theory and Lie algebras including their quantum analogues; methods of group representation theory. Results and their novelty - it is proposed the methods of construction of unimodular matrix Baker-Akhiezer functions on the complex plane; solving mixed problems for a quantum laser amplifier and a long attenuator; structural analysis of the front of dispersion shock waves; approximation of solutions of the Bryan-Pidduck equation for asymmetric helical flows and an infinite number of tornado-like flows; solution of inverse problems of perturbation theory with presentation of formulas for reconstruction of matrices and Sturm-Liouville operator on a finite interval; a complete description of all Uq(sl2) -symmetries of the Laurent extansion of the quantum plane and the disk; characterization of the half-infinity of von Neumann algebras generated by representations of an infinite symmetric group. Product Description popup.authors popup.nrat_date 2021-02-05 Close