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We introduce the two-dimensional Gross-Pitaevskii/nonlinear-Schrodinger (GP/NLS) equation with the self-focusing nonlinearity confined to two identical circles, separated or overlapped. The model can be realized in terms of Bose-Einstein…
In this paper, we study the regularities of solutions of nonlinear stochastic partial differential equations in the framework of Hilbert scales. Then we apply our general result to several typical nonlinear SPDEs such as stochastic Burgers…
The construction of stochastic solutions for nonlinear partial differential equations is a powerful method to obtain new exact results and to develop efficient numerical algorithms, in particular when domain decomposition techniques are…
Starting with some fundamental concepts, in this article we present the essential aspects of spectral methods and their applications to the numerical solution of Partial Differential Equations (PDEs). We start by using Lagrange and…
This work is devoted to the construction of slowly rotating neutron stars in the framework of the nonminimal derivative coupling sector of Horndeski theory. We match the large radius expansion of spherically symmetric solutions with…
We study a model elliptic pseudo-differential equation and simplest boundary value problems for a half-space and a special cone in Sobolev--Slobodetskii spaces which have different smoothness with respect to separate variables. Sufficient…
We propose a high-order spacetime wavelet method for the solution of nonlinear partial differential equations with a user-prescribed accuracy. The technique utilizes wavelet theory with a priori error estimates to discretize the problem in…
$\ell$-boson stars are static, spherical, multi-field self-gravitating solitons. They are asymptotically flat, finite energy solutions of Einstein's gravity minimally coupled to an odd number of massive, complex scalar fields. A previous…
We present a simulation code which can solve broad ranges of partial differential equations in a full sphere. The code expands tensorial variables in a spectral series of spin-weighted spherical harmonics in the angular directions and a…
An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary…
We obtain the well-posedness and Schauder estimates for a class of system of linear, quasi-linear and non-linear second order partial differential equations. We deduce existence and uniqueness of a global smooth solution of a non-linear and…
The advection-diffusion and wave equations are the fundamental equations governing any physical law and therefore arise in many areas of physics and astrophysics. For complex problems and geometries, only numerical simulations can give…
This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…
In this manuscript the three types of late-time behavior of spherically symmetric Boson Stars are presented, these are: stable configurations, unstable bounded that collapse to form black holes and unstable unbounded that explode. The…
Compton scatter tomography is an emerging technique with attractive applications in several fields in imaging such as non-destructive testing and medical scanning. In this paper, we introduce a novel modality in three dimensions with a…
We propose that stable boson stars generically fall within an infinite-parameter family of solutions that oscillate on any number of non-commensurate frequencies. We numerically construct two-frequency solutions and explore their parameter…
We investigate numerically light propagation in a single spiral waveguide formed in a nonlinear photorefractive medium for a low spatial frequency of the waveguide rotation. We present the general procedure for finding solitonic solutions…
A new method is proposed to divide a spherical surface into equal-area cells. The method is based on dividing a sphere into several latitudinal bands of near-constant span with further division of each band into equal-area cells. It is…
We construct analytical phase-space solutions for perturbations of flat disks by performing a power series expansion for the radius and the velocity coordinates. We show that this approach translates into an elegant mathematical formulation…
We apply the asymptotic iteration method (AIM) to obtain the solutions of Schrodinger equation in the presence of Poschl-Teller (PT) potential. We also obtain the solutions of Dirac equation for the same potential under the condition of…