Bogolyubov N. N.
Generalized de Rham-Hodge complexes, the related characteristic Chern classes, and some applications to integrable multidimensional differential systems on Riemannian manifolds
Ukr. Mat. Zh. - 2007. - 59, № 3. - pp. 327–344
We study the differential-geometric aspects of generalized de Rham-Hodge complexes naturally related to integrable multidimensional differential systems of the M. Gromov type, as well as the geometric structure of the Chern characteristic classes. Special differential invariants of the Chern type are constructed, their importance for the integrability of multidimensional nonlinear differential systems on Riemannian manifolds is discussed. An example of the three-dimensional Davey-Stewartson-type nonlinear integrable differential system is considered, its Cartan type connection mapping, and related Chern-type differential invariants are analyzed.
A bilocal periodic problem for the Sturm-Liouville and Dirac operators and some applications to the theory of nonlinear dynamical systems. I
Ukr. Mat. Zh. - 1990. - 42, № 6. - pp. 794–800
Ukr. Mat. Zh. - 1986. - 38, № 6. - pp. 774–778
N. N. Bogolyubov's quantum method of generating functionals in statistical physics: The current Lie algebra, its representations, and functional equations
Ukr. Mat. Zh. - 1986. - 38, № 3. - pp. 284–289
Ukr. Mat. Zh. - 1965. - 17, № 3. - pp. 3-15
Ukr. Mat. Zh. - 1961. - 13, № 3. - pp. 3-12
An asymptotic method of constructing periodic solutions is developed for differential equations of the $n$-th order containing a small parameter. The method makes use of expansions in integral powers of the small parameter. A method of investigating the stability of the resulting solutions is presented. The convergence of the expansions is proved.