Related papers: The qualitative behavior at a vortex point for the…
Consideration here is a generalized $\mu$-type integrable equation, which can be regarded as a generalization to both the $\mu$-Camassa-Holm and modified $\mu$-Camassa-Holm equations. It is shown that the proposed equation is formally…
We investigate how topological Chern numbers can be defined when single-particle states hybridize with continua. We do so exemplarily in a bosonic Haldane model at zero temperature with an additional on-site decay of one boson into two and…
The 2d Boussinesq equations model large scale atmospheric and oceanic flows. Whether its solutions develop a singularity in finite-time remains a classical open problem in mathematical fluid dynamics. In this work, blowup from smooth…
In this paper, we consider the Cauchy problem for a class of weakly dissipative Camassa-Holm equations in nonhomogeneous Besov spaces. First, we prove that the Cauchy problem admits a unique global strong solution in Besov spaces with…
We consider the semilinear wave equation with power nonlinearity in one space dimension. We consider an arbitrary blow-up solution $u(x,t)$, the graph $x\mapsto T(x)$ of its blow-up points and ${\cal S}\subset {\mathbb R}$ the set of all…
The cooling of a Bose gas in finite time results in the formation of a Bose-Einstein condensate that is spontaneously proliferated with vortices. We propose that the vortex spatial statistics is described by a homogeneous Poisson point…
In this paper we consider a system of equations that describes a class of mass-conserving aggregation phenomena, including gravitational collapse and bacterial chemotaxis. In spatial dimensions strictly larger than two, and under the…
Three examples of non-dissipative yet cumulative interaction between a single wavetrain and a single vortex are analysed, with a focus on effective recoil forces, local and remote. Local recoil occurs when the wavetrain overlaps the vortex…
We study the effect of a Chern-Simons term on the electrically charged and spinning solitons of several $U(1)$ gauged models in $2+1$ dimensions. These are vortices of complex scalar field theories, both with and without symmetry breaking…
The multivariable theory of nucleation [J. Chem. Phys. 124, 124512 (2006)] is applied to the problem of vapor bubbles formation in pure liquids. The presented self-consistent macroscopic theory of this process employs thermodynamics…
The hydrogen atom in two dimensions, described by a Schr\"odinger equation with a Chern-Simons potential, is numerically solved. Both its wave functions and eigenvalues were determined for small values of the principal quantum number $n$.…
We define a formalism of a self-consistent description of the ground state of a weakly interacting Bose system, accounting for higher order terms in expansion of energy in the diluteness parameter. The approach is designed to be applied to…
We introduce a new family of p-adic non-linear evolution equations. We establish the local well-posedness of the Cauchy problem for these equations in Sobolev-type spaces. For a certain subfamily, we show that the blow-up phenomenon occurs…
This paper considers a class of non-local equations that are weakly dispersive perturbations of the inviscid Burgers equation, which includes the Fornberg-Whitham equation as a special case. We precise the known results on finite time…
We investigate the presence of vortex structures in generalized Maxwell-Higgs and Chern-Simons-Higgs models in the three-dimensional spacetime. Despite the important difference between the Maxwell and Chern-Simons dynamics, we have been…
In the context of many-body interacting systems described by a topological Hamiltonian, we investigate the robustness of the Chern number with respect to different sources of error in the self-energy. In particular, we analyze the…
We study a non-Abelian Chern-Simons gauge theory in $ 2+ 1$ dimensions with the inclusion of an anomalous magnetic interaction. For a particular relation between the Chern-Simons (CS) mass and the anomalous magnetic coupling the equations…
We use a Bogoliubov-de Gennes (BdG) formulation to describe a single vortex in a neutral fermionic gas. It is presumed that the attractive pairing interaction can be arbitrarily tuned to exhibit a crossover from BCS to Bose-Einstein…
The self-duality equations of Chern-Simons Higgs theory in a background curved spacetime are studied by making use of the U(1) gauge potential decomposition theory and $\phi$-mapping method. The special form of the gauge potential…
In the present paper, we consider the Chern-Simons-Schr\"{o}dinger system \begin{equation} \left\{ \begin{aligned} &-\varepsilon^{2}\Delta u+V(x)u+(A_{0}+A_{1}^{2}+A_{2}^{2})u=|u|^{p-2}u,\,\,\,\,x\in \mathbb{R}^2,\\ &\partial_1 A_0 = A_2…