It is shown how to set up a mathematically elegant and fully relativistic superfluid model that can provide a realistic approximation (neglecting small anisotropies due to crust solidity, magnetic fields, et cetera, but allowing for the regions with vortex pinning) of the global structure of a rotating neutron star, in terms of just two independently moving constituents, one of which represents the differentially rotating neutron superfluid, while the other part represents the combination of all the other ingredients, including the degenerate electrons, the superfluid protons in the core, and the ions in the crust, whose electromagnetic interactions will tend to keep them locked together in a state of approximately rigid rotation. Order of magnitude estimates are provided for relevant parameters such as the resistive drag coefficient and the maximum pinning force.Comment: 35 pages, Latex, no figure, submitted to M.N.R.A.

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The problem of determination of the maximum of second harmonic generation in the potential well containing a rectangular barrier is considered. It is shown that, in general, the problem of finding the ensemble of structures with equidistant first three levels has two types of solutions. For the first type the second and third energy levels are located above a rectangular barrier, and for the second type the third level is located above the barrier only. It is also shown, that generation corresponding to the second type of solution always is less than generation for the first one. Taking into account the effective mass changes the problem of finding the generation maximum for a finite depth well is exactly solved.

We have derived the closed system of covariant equations which describe the motion of quantum vortices regarded as a two-dimensional polarized liquid. We have written the covariant expressions of the forces acting on the vortices; from the equilibrium condition of these forces, we have deduced the equation satisfied by the velocity field of the fluid. It is shown that this velocity field depends, respectively, on the friction coefficient, the density of vortices, and the superconducting current. From this closed system of equations, we have derived the relaxation equation and solved it when a variable magnetic field is applied.