Аннотация:To introduce novel ways of manipulation of the skyrmions dynamics we need to develop new fundamental models. The many-particle quantum hydrodynamics allows us to study inter-skyrmion interactions in the approximation of point-particle skyrmions, which were discovered in the multiferroic insulators, where the spiral magnetic structure is accompanied by finite electric dipole moment. We propose the new model of many-particle quantum hydrodynamics for the dipolar skyrmions with dipole-dipole interaction, in the presence of electric and magnetic field gradients. Based on the developed model we find the new way to control the positions of skyrmions, using the crossed gradients of magnetic and electric fields
or novel magneto-electric Hall effect. The influence of non-uniform magnetic field provides circular motion of the dipolar skyrmion in the plane with the frequency determined by the derivative of the external magnetic field and the amplitude of the dipole moment. We study the wave processes in the system of skyrmions. We investigate the hydrodynamic waves in the gas of skyrmions in crossed non-uniform electric and magnetic fields, and predict generation of the new type of hydrodynamic waves and the instabilities. Also, we predict the new type of polarization waves in the gas of rigid skyrmions with dipole-dipole interaction.