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In order to find analytically the travelling waves of partially integrable autonomous nonlinear partial differential equations, many methods have been proposed over the ages: "projective Riccati method", "tanh-method", "exponential method",…
It is shown that the Kerr-Newman solution, representing charged and rotating stationary black holes, admits analytic extension at the singularity. This extension is obtained by using new coordinates, in which the metric tensor becomes…
In this article, we investigate the weighted Steklov eigenvalue problem and the weighted Schr\"odinger--Steklov eigenvalue problem in outward cuspidal domains. We prove the solvability of these spectral problems in both linear and…
We present a proposal for the realization of entanglement Hamiltonians in one-dimensional critical spin systems with strongly interacting cold atoms. Our approach is based on the notion that the entanglement spectrum of such systems can be…
In this paper, analytical solutions describing static and spherically symmetric sources in the decoupling limit of massive gravity are derived. We analyze the model parameter range and specify when a Vainshtein mechanism is possible.…
We analyze numerically the existence of regular stationary rotating hairy black holes within the framework of general relativity, which are the result of solving the Einstein-Klein-Gordon system for a complex-valued scalar field under…
In the framework of non-riemannian geometry, we derive exact static vacuum solutions of the field equations obtained from the full equivalent version of the Einstein-Hilbert action when torsion degrees of freedom are taken into account. By…
An exact, number-conserving solution to the generalized, orbit-dependent pairing problem is derived by introducing an infinite-dimensional algebra. A method for obtaining eigenvalues and eigenvectors of the corresponding Hamiltonian is also…
On a bounded smooth domain we study solutions of a semilinear elliptic equation with an exponential nonlinearity and a Hardy potential depending on the distance to the boundary of the domain. We derive global a priori bounds of the…
We survey many of the important properties of spherically symmetric spacetimes as follows. We present several different ways of describing a spherically symmetric spacetime and the resulting metrics. We then focus our discussion on an…
We show that there exists a family of analytic convex global rotating solutions for the vortex patch equations, bifurcating from ellipses. As a byproduct, the analyticity proof can also be adapted to the rotating patch solutions bifurcating…
The most general set of static and spherically symmetric solutions for conformal Killing gravity coupled to Maxwell fields is presented in closed form. These solutions, depending on six parameters, include non-asymptotically flat black…
In the context of the Einstein-scalar-Gauss-Bonnet theory, with a general coupling function between the scalar field and the quadratic Gauss-Bonnet term, we investigate the existence of regular black-hole solutions with scalar hair. Based…
We consider a stochastic nonlinear Schr\"odinger equation with multiplicative noise in an abstract framework that covers subcritical focusing and defocusing stochastic NLS in $H^1$ on compact manifolds and bounded domains. We construct a…
Seven new solutions to the interior static and spherically symmetric Einstein's field equations (EFE) are found and investigated. These new solutions are a generalisation of the quadratic density fall-off profile of the Tolman VII solution.…
Tetrad based equation for Dirac-K\"{a}hler particle is solved in spherical coordinates in the flat Minkocski space-time. Spherical solutions of boson type (J =0,1,2,...) are constructed. After performing a special transformation over…
In the framework of a simple gravitational theory that contains a scalar field minimally coupled to gravity, we investigate the emergence of analytic black-hole solutions with non-trivial scalar hair of secondary type. Although it is…
In many time-harmonic electromagnetic wave problems, the considered geometry exhibits an axial symmetry. In this case, by exploiting a Fourier expansion along the azimuthal direction, fully three-dimensional (3D) calculations can be carried…
In this essay, we argue that an observer outside the horizon can reconstruct the geometry of a black hole's interior through external measurements. This procedure builds on recent studies of the holographic duality of timelike entanglement…
The Slater-type orbital basis with non-integer principal quantum numbers is a physically and mathematically motivated choice for molecular electronic structure calculations in both non-relativistic and relativistic theory. The…