We investigate the electromagnetic fields in the vacuum exterior of a rotating relativistic star endowed with a magnetic dipole moment, and with the stellar surface behaving as a perfect conductor. While the stellar rotation is treated in the slow-approximation of general relativity, we do not restrict our attention to slowly rotating electromagnetic fields, and take our analysis beyond the low...

This study describes a semi-analytic solution of planar radiative shock waves in which the radiation model is grey nonequilibrium diffusion. The solution may be used to verify radiation-hydrodynamics codes. Comparisons are made with the equilibrium diffusion solutions of Lowrie and Rauenzahn [1]. Although the physics of radiative shocks are fairly well known, previous solutions have been approx...

We examined the physical origin of the colour–magnitude relation of elliptical galaxies in clusters of galaxies in the hierarchical clustering scenario by using a semi-analytic model of galaxy formation. The semi-analytic model includes some physical processes connected with the galaxy formation, such as merging histories of dark haloes, gas cooling, star formation, supernova feedback, mergers ...

This paper reviews the efforts to construct (or prove the impossibility of) singular solutions of the Euler equations for three dimensional incompressible flow. A semi-analytic approach to this problem is formulated based on numerical computation of complex traveling wave solutions, followed by perturbation construction of a real solution, for axisymmetric flow with swirl. The perturbation anal...

Two important cases, where boundary conditions and solutions of the well-known integrable equations on a semi-strip are uniquely determined by the initial conditions, are rigorously studied in detail. First, the case of rectangular matrix solutions of the defocusing nonlinear Schrödinger equation with quasi-analytic boundary conditions is dealt with. (The result is new even for a scalar nonline...

In this paper, we propose the application of the general homotopy method (GHM) to obtain rational solutions of nonlinear differential equations. It delivers a high precision representation of the nonlinear differential equation using a few linear algebraic terms. In order to assess the benefits of this proposal, three nonlinear problems are solved and compared against other semi-analytic method...

Cosmic strings are topological defects thought to have formed early in the life of the universe. If such objects exist, a study of their interaction with black holes is of interest. The equations of motion of a cosmic string have the form of highly non-linear wave equations. General analytic solutions, except for motion in certain backgrounds such as flat and shockwave spacetimes, remain unknow...

In this paper, stochastic age-structure population system with jump are studied. It is proved that the semi-implicit Euler approximation solutions converge to the analytic solution for the stochastic age-structured population system with Poisson jump. The analysis use ˆ Ito s ′ formula, Burkholder-DavisGundy's inequality, Gronwall's lemma and some inequalities for our purposes.