Related papers: Some vortex solutions in the extended Skyrme-Fadde…
Analytic methods to investigate periodic orbits in galactic potentials. To evaluate the quality of the approximation of periodic orbits in the logarithmic potential constructed using perturbation theory based on Hamiltonian normal forms.…
We calculate the energy of a Yang-Mills vortex as function of its magnetic flux or, else, of the Wilson loop surrounding the vortex center. The calculation is performed in the 1-loop approximation. A parallel with a potential as function of…
The possibility of the decomposition of the three dimensional (3D) Gross-Pitaevskii equation (GPE) into a pair of coupled Schr\"{o}dinger-type equations, is investigated. It is shown that, under suitable mathematical conditions, solutions…
Stochastic Navier-Stokes equations in 2D and 3D possibly unbounded domains driven by a multiplicative Gaussian noise are considered. The noise term depends on the unknown velocity and its spatial derivatives. The existence of a martingale…
Vortices represent a class of topological solitons arising in gauge theories coupled with complex scalar fields, holding significant importance across various domains of modern physics. In this paper we establish the existence of vortex…
Analytic solutions of the Teukolsky equation in Kerr geometries are presented in the form of series of hypergeometric functions and Coulomb wave functions. Relations between these solutions are established. The solutions provide a very…
Quantum vortices in superfluids have been an important research area for many decades. Naturally, research on this topic has focused on two and three-dimensional superfluids, in which vortex cores form points and lines, respectively. Very…
The numerical algorithm of the inverse quantum scattering is developed. This algorithm is based on the Marchenko theory, and includes three steps. The first one is the algebraic Pade approximation of the unitary S-matrix, what is realized…
The Kitaev model realizes a quantum spin liquid where the spin excitations are fractionalized into itinerant Majorana fermions and localized $\mathbb{Z}_2$ vortices. Quantum entanglement between the fractional excitations can be utilized…
We derive tight expressions for the maximum number of $k$-faces, $0\le k\le d-1$, of the Minkowski sum, $P_1+P_2+P_3$, of three $d$-dimensional convex polytopes $P_1$, $P_2$ and $P_3$, as a function of the number of vertices of the…
As is well-known, two-dimensional and three-dimensional superfluids under rotation can support topological excitations such as quantized point vortices and line vortices respectively. Recently, we have studied how, in a hypothetical…
We revisit the two vortex merger problem (symmetric and asymmetric) for the Navier-Stokes equations using the core growth model for vorticity evolution coupled with the passive particle field and an appropriately chosen time-dependent…
We investigate vortex solutions to the Abelian Higgs field equations in a four dimensional de Sitter spacetime background. We obtain both static and dynamic solutions with axial symmetry that are generalizations of the Nielsen-Olesen gauge…
Vortices symmetric with respect to simultaneous parity and time reversing transformations are considered on the square lattice in the framework of the discrete nonlinear Schr\"{o}dinger equation. The existence and stability of vortex…
We obtain classes of black hole solutions constructed from multiplets of scalar fields in 2+1 / 3+1 dimensions. The multi-component scalars don't undergo a symmetry breaking so that only the isotropic modulus is effective. The Lagrangian is…
This paper is mainly concerned with the inverse scattering problem of determining the unknown potential for the classical Schr\"odinger equation in two and three dimensions. We establish the increasing stability of the inverse scattering…
This paper systematically explains how to apply the invariant subspace method using variable transformation for finding the exact solutions of the (k+1)-dimensional nonlinear time-fractional PDEs in detail. More precisely, we have shown how…
An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems…
In the extended (1 + 4) -dimensional space (T;X,Y,Z,S)-(time-space-interval) it is considered a model joining electromagnetic and gravitational fields. For the equations circumscribing these fields, the exact solutions appropriated to dot…
We prove the existence of smooth solutions to the Gross-Pitaevskii equation on $\mathbf{R}^3$ that feature arbitrarily complex quantum vortex reconnections. We can track the evolution of the vortices during the whole process. This permits…