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The general construction of semiclassically concentrated solutions to the Hartree type equation, based on the complex WKB-Maslov method, is presented. The formal solutions of the Cauchy problem for… (More)

A method of noncommutative integration of linear partial differential equations that is analogous to noncommutative integration of finite-dimensional Hamiltonian systems is proposed. The method is… (More)

We consider two random hypergraphs with n vertices and M D M.n/ edges among which Mi D Mi .n/ edges consist of i non-ordered vertices, i D 0; 1; : : : ; m, M D M0 C M1 C : : : C Mm. The choice of… (More)

We have investigated the pattern formation in systems described by the nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation for the cases where the dimension of the pattern concentration domain is… (More)

A self-consistent model of the dynamics of a cellular population described by the generalized Fisher–Kolmogorov–Petrovskii–Piskunov equation with nonlocal competitive losses and interaction with the… (More)

Within the formalism of the Fokker-Planck equation, the influence of nonstationary external force, random force, and dissipation effects on the kink dynamics is investigated in the sine-Gordon model.… (More)

With the help of energy analysis suggested by McLaughlin and Scott for the sine-Gordon equation, evolution of kink velocity modeling the propagation of a local conformational perturbation along the… (More)

A semiclassical approximation approach based on the Maslov complex germ method is considered in detail for the one-dimensional nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov (Fisher–KPP) equation… (More)

A class of nonlinear symmetry operators has been constructed for the many-dimensional nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation quadratic in independent variables and derivatives. The… (More)

Based on the ideology of the Maslov complex germ theory, a method has been developed for finding an exact solution of the Cauchy problem for a Hartree-type equation with a quadratic potential in the… (More)