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Information × Registration Number 0201U001192, 0198U001993 , R & D reports Title Analitical and symmetry methods of investigation of differential models of mathematical physics popup.stage_title Head Nikitin A.G., Registration Date 22-01-2001 Organization Institute of mathematics NAS of Ukraine popup.description2 The object for the investigation is nonlinear models of mathematical physics. The aim of the work is creation of new effective methods for analysis of symmetry of differential equations, construction of exact solutions, group classification of equations of mathematical physics, creation of group-theoretical basis for modern models in mathematical physics. The methods for investigation are modern methods of the group analysis and representation theories of generalized Lie algebras. Wide classes of exact solutions for a number of nonlinear multidimensional equations of mathematical physics and mathematical biology were constructed using the concept of conditional symmetry. Operators of higher and conditional symmetries were found for linear and nonlinear Schrodinger equations. Coordinate systems were described for which solutions with separated variables exists for the n-dimensional Schrodinger equations. Classification of quasi-exactly solvable Schrodinger equations was accomplished in the framework of the conditional symmetry concept. New methods for construction of families of exact solutions for nonlinear multidimensional partial differential equations, that are based on combination of nonlocal discrete symmetries. Extended super- and parasupersymmetry of the quantum mechanics equations, new motion integrals were found for two-particle equations. New irreducible representations for Poincare super- and parasuperalgebras that include arbitrary number of ordinary and central charges. Employment of polyparabolical linear evolution equation for mathematical description of special conditions of heat and mass transfer was justified. Solutions for integral-differential heat equation for media with hereditary properties (heat memory) were obtained. Product Description popup.authors popup.nrat_date 2020-04-02 Close