Processes of interaction of capillary waves were considered both numerically and analytically: merging of two waves into one and wave on the ring (in Fourier space, isotropic spectrum) into larger diameter ring. It was shown numerically, that these processes are the leading ones and other processes with respect to them are at least weaker if manifest themselves at all. In the case of isotropic turbulence of capillary waves the formation of wave turbulence Zakharov-Filonenko spectrum is demonstrated. It was also shown, that in this case one should be cautious about statements of the locality theorem.

It is well known that the anomalous Hall effect in ferromagnetic and strongly paramagnetic metals in addition to electron skew scattering on impurities is determined by internal mechanism linked to the Berry curvature, a quantum-mechanical property of the electron states of a perfect crystal. Experimentally, however, it has been established that the Berry curvature does not play any role in the Hall resistance of the ferromagnet URhGe. URhGe is so called altermagnetic ferromagnet which crystal symmetry includes operation of time inversion only in combination with rotations and reflections. The explanation for strictly zero Berry curvature of electronic states in this material lies in the non-symmorphic symmetry of its crystal lattice.

The pressure-temperature phase diagram of superconducting UTe${}_2$ with three lines of the second- order phase transitions cannot be explained in terms of successive transitions to superconducting states with a decrease in symmetry. The problem is solved using a two-band description of the superconducting state of UTe${}_2$.

The sinh-Gordon model is considered on a multi-sheeted Riemann surface with a plane metric and cuts, which connect the sheets. Such a model can be considered as a few copies of the sinh-Gordon model on the plane, connected by special operators (twist operators) that correspond to the end points of the cuts, which are branch points. More complicated operators, composite branch-point twist operators can be considered. They correspond to local operators placed to the branch points. In the present work we calculate form factors of a few series of such operators in the semiclassical limit. The semiclassical approach does not use quantum integrability, but essentially based on exact solutions of the classical model. It allowed us to understand better the renormalization of the local operators.

We study triggered by an a.c. external electric field weakly nonlinear stages of flexoelectric instability in nematic liquid crystals. The instability occurs at a finite wave vector. We analyze behavior on time scales much larger than the period of the external electric field. We focus on the case where the increment of the most-unstable mode has an imaginary part, so-called Hopf bifurcation. The existence of such regime was established in our previous work [E.S. Pikina, A.R. Muratov, E.I.Kats, V.V. Lebedev, Dynamic flexoelectric instabilities in nematic liquid crystals, Phys. Rev. E, 110, 024701 (2024)]. Then above the instability threshold a variety patterns of nematic director distortions could appear including standing and travelling structures. Our numerical simulations based on the full nonlinear electro-nematodynamics system of equations. We found that the stable dynamic pattern in the vicinity of the Hopf bifurcation travelling oblique rolls of the nematic director distortions. The establishment of this regime occurs abnormally slowly, which is determined not only by the critical Landau-like slowdown of dynamics, but also by the presence of a long-lived intermediate unstable but long-lived dynamic patterns oscillating in time (standing but not traveleling rolls). Depending on liquid crystal material parameters, the bifurcation corresponding to the formation of the travelling oblique rolls, can be soft (i.e.continues, ‘’critical’’ or close to ‘’tricritical’’ one), or hard (discontinues).