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Semiclassical approximation for the integral-differential equations of mathematical physics
- Semiclassical asymptotics for the nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation concentrated at the point and on the one-dimensional manifold are found;
- Symmetries and symmetry operators for the nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation are calculated;
- The discrepancy of semiclassical asymptotics for the nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation is investigated;
- Large-time asymptotics are found for the nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation;
Abrikosov vortices on curved nanostructures
- The special features at nano- and microscales of the vortex dynamics on superconducting cylindrical Nb tubes produced by the roll-up (self-rolling) technique are considered. It is shown that for certain values of the magnetic field, two different trajectories are possible for a moving vortex, i.e., a bifurcation phenomenon occurs. This phenomenon is explained.
- An inhomogeneous transport current, which is introduced through multiple electrodes in an open Nb microtube, is shown to lead to a controllable branching of the vortex nucleation period. The detailed mechanism of this branching is analyzed using the time-dependent Ginzburg–Landau equation.;
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