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Information × Registration Number 0212U000432, 0109U001520 , R & D reports Title Classification of the symmetry properties and construction of some classes of exact solution of the nоnlinear mathematical physics equations. popup.stage_title Head Serov Mykola Ivanovych, Registration Date 10-02-2012 Organization Polava National Technical University named in the honour of Yuri Kondratyuk popup.description2 The subject of study is the nonlinear equations of mathematical physics. Object - symmetry properties of nonlinear equations of mathematical physics. The Purpose of Research Work - a classification of symmetry properties and construction of exact solutions of nonlinear partial differential equations. Methods of Rresearch Work - the classic Lie-Ovsyannikov and conditional symmetry methods. Solutions of the fundamental goals in the general problem framework are made in the project: - conducted the classification of symmetry properties and the investigation of one-dimensional conditional symmetry of reaction-diffusion-convection equation, which is used to describe a lot of physical processes: modeling of diffusion processes, heat conduction, energy transfer in the plasma, solutions distribution in the soil, the movement of liquids in porous medium and other physical and biochemical processes. Class of reaction diffusion-convection equation contains such well-known equation as the heat equation, Burgers equation and etc. - searched out the soliton solutions and non-local formula to generate solutions of one-dimensional and multidimensional sine-Gordon equation.On the geometric point of view, the sine-Gordon equation occured in differential geometry in the late nineteenth century and is connected with the problem of constructing Chebyshevsky meshes on surfaces of negative curvature. In physics sine-Gordon equation was applied in the theory of dislocations by J. Frenkel and T. Kantorova. It describes the distribution of conditional or actual spins in different systems in physics. Sine-Gordon equation is one of the most famous equations of soliton theory, development of which originates from the observation of such physics phenomena as '' solitary ware'' (solitary waves) by British engineer J.S. Russell in 1834. Later, in 1965 this wave in the N.J.Zabusky and M.D.Kruska was called the soliton; - conducted the classification of symmetry properties of the chemotaxis equations system. The processes of symmetric distribution of bacterial population waves, when the chemotaxis rings remain sharply outlined form and move at constant speed, which depends on the mobility of bacteria and chemotaxis properties are described in modern biophysical researches of the chemotaxis equations system;-the classification of the symmetry properties in respect to the Poincare algebra and the conform algebra for the quasi-wave equation was made. Product Description popup.authors Блажко Л.М. Омелян О.М. Плюхін О.Г. Рассоха І.В. Сєрова М.М. popup.nrat_date 2020-04-02 Close