相关论文: Solutions of all one-dimensional wave equations wi…

We find the most general spherically symmetric non singular black hole solution in a special class of teleparallel theory of gravitation. If $r$ is large enough, the general solution coincides with the Schwarzschild solution. Whereas, if…

Quantum mechanical scalar particle with polarizability is considered in the presence of the Coulomb field. Separation of variables is performed with the use of Wigner $D$-functions, the radial system of 15 equations is reduced to a single…

For space-times with two spacelike isometries, we present infinite hierarchies of exact solutions of the Einstein and Einstein--Maxwell equations as represented by their Ernst potentials. This hierarchy contains three arbitrary rational…

A new proposed one dimensional time independent Schr\"odinger equation is solved completely using shape invariance method. The corresponding potential is given by V_(x,A,B) =-A(sechpx)^2 - 6Bp(sech6px)^2+(tanhpx-6tanh6px)^2 with…

We present simple, analytic solutions to the Einstein-Maxwell equation, which describe an arbitrary number of charged black holes in a spacetime with positive cosmological constant $\Lambda$. In the limit $\Lambda=0$, these solutions reduce…

We present n-dimensional vortex-ring-like and potential-like solutions with unusual properties related to some elliptical differential equations with compact sources. Solutions have almost 3- or 2-dimensional behaviour in the spaces with…

The one-dimensional Schroedinger's equation is analysed with regard to the existence of exact solutions for decatic polynomial potentials. Under certain conditions on the potential's parameters, we show that the decatic polynomial potential…

We prove the existence of global solutions to the energy-supercritical wave equation in R^{3+1} u_{tt}-\Delta u + |u|^N u = 0, u(0) = u_0, u_t(0) = u_1, 4<N<\infty, for a large class of radially symmetric finite-energy initial data.…

Version 1: The well known Eckart's singular s-wave potential is PT-symmetrically regularized and continued to the whole real line. The new model remains exactly solvable and its bound states remain proportional to Jacobi polynomials. Its…

The main result of this research Monograph is the existence of small amplitude time quasi-periodic solutions for autonomous nonlinear wave equations $$ u_{tt} - \Delta u + V(x) u + g(x, u) = 0 \, , \quad x \in T^d \, , \quad g (x,u) = a(x)…

We consider Einstein-Maxwell-self-interacting scalar field theory described by a potential $V\left( \phi \right) $ in $2+1-$dimensions. The self-interaction potential is chosen to be a highly non-linear double-Liouville type. Exact…

We study a class of Calogero-Sutherland type one dimensional N-body quantum mechanical systems, with potentials given by $$ V( x_1, x_2, \cdots x_N) = \sum_{i <j} {g \over {(x_i - x_j)^2}} - \frac{g^{\prime}}{\sum_{i<j}(x_i - x_j)^2} +…

The Cauchy problem for two dimensional difference wave operators is considered with potentials and initial data supported in a bounded region. The large time asymptotic behavior of solutions is obtained. In contrast to the continuous case…

A solvable 2-dimensional conformally invariant midi-superspace model for black holes is obtained by imposing spherical symmetry in 4-dimensional conformally invariant Einstein gravity. The Wheeler-DeWitt equation for the theory is solved…

In this paper, we obtain several asymptotic profiles of solutions to the Cauchy problem for structurally damped wave equations $\partial_{t}^{2} u - \Delta u + \nu (-\Delta)^{\sigma} \partial_{t} u=0$, where $\nu >0$ and $0< \sigma \le1$.…

We prove local unique solvability of the wave equation for a large class of weakly singular, locally bounded space-time metrics in a suitable space of generalised functions.

We present a class of confining potentials which allow one to reduce the one-dimensional Schroodinger equation to a named equation of mathematical physics, namely either Bessel's or Whittaker's differential equation. In all cases, we…

Canonical quantization of spherically symmetric initial data which is appropriate to classical interior black hole solutions in four dimensions is carried out and solved exactly without gauge fixing the remaining kinematic Gauss Law…

We discuss, in a pedagogical way, how to solve for relativistic wave functions from the radial Dirac equations. After an brief introduction, in Section II we solve the equations for a linear Lorentz scalar potential, V_s(r), that provides…

We present a general solution of the coupled Einstein-Maxwell field equations (without the source charges and currents) in three spacetime dimensions. We also admit any value of the cosmological constant. The whole family of such…