| RUS ENG |
| Full version |
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| PEOPLE |
| Berkovich Lev Meilikhovich |
| Associate professor |
| Candidate of physico-mathematical sciences (1967) |
1) All mathematical laws of a modification of a mass in classical non-stationary problem of celestial mechanics (problem of Gylden–Meshcherskii) are found.
2) First systematic exposition of a method of factorization differential operators in synthesis with a method of transformation of variables. Thev outcomes are applied to an integration of the linear differential equations with variables coefficients. The solution of classical problems of G.-H. Halphen about equivalence and classification linear equations of order $n>2$ is given.
3) The exact invariant solutions for the equation Kolmogorov–Petrovskii–Piskunov and some other nonlinear heat and diffusion equations. For want of it methods of the group analysis and factorization ODE.
4) The general class of nonlinear nonautonomous ODE of order $n$ is constructed, supposing a factorization through nonlinear differential operators of the first order. This class simultaneously supposes a exact linearization to the autonomous equations. The constructed class of the equations is applied to some integrable dynamical systems: Liouvillian's systems, and some systems of a hydrodynamical type, and systems of a right body.
5) The generalization of inhering S. Lie of a nonlinear principle of superposition for solutions of nonlinear ODE is considered. The new nonlinear superposition principle is applied for effective integration of nonlinear evolutionary equations of mathematical physics.
