In this paper, we study domain decomposition preconditioners for multiscale elliptic problems in high contrast media. We construct preconditioners such that the condition number of the preconditioned system is independent of media contrast. For this purpose, multiscale spaces for the interpolation on the coarse grid is developed using a local weighted spectral problem. A main observation is tha...

We consider the approximation of a Schrödinger eigenvalue problem arising from the modeling of semiconductor nanostructures by a finite volume method in a bounded domain Ω ⊂ R. In order to prove its convergence, a framework for finite dimensional approximations to inner products in the Sobolev space H 0 (Ω) is introduced which allows to apply well known results from spectral approximation theor...

We study the Zeeman–Stark effect problem in hydrogen atom located an electromagnetic field by using irreducible representations of Karasev–Novikova algebra with quadratic commutation relations. find asymptotics a series eigenvalues and corresponding eigenfunctions near lower boundaries spectral clusters.

In this paper we numerically investigate the effect of relative phase on thestability of temporal bright solitons in a Nano PT- Symmetric nonlinear directionalcoupler (NLDC) by considering gain in bar and loss in cross. We also study the effect ofrelative phase on the output perturbed bright solitons energies, in the range of   0 to 180 . By using perturbation theory three eigenfunctions an...

We construct rogue wave solutions on the double-periodic background for Hirota equation through onefold Darboux transformation formula. consider two types of as seed solutions. identify squared eigenfunctions and eigenvalues that appear in formula an algebraic method with eigenvalues. then desired solution steps. In first step, we create waves background. second build top this solution. present...

We consider a Dirichlet spectral problem for second order differential operator, with piecewise constant coefficients, in domain ?? the plane R2. Here is ??????, where ? fixed bounded boundary ?, ?? curvilinear band of width O(?), and ?=??????. The density stiffness constants are ??m?t ??t respectively this band, while they 1 ?; t?1, m>2, ? small positive parameter. address asymptotic behavior,...

Relying upon tools from the theory of integrable systems, we discuss linear instability Kuznetsov–Ma breathers and Akhmediev focusing nonlinear Schrödinger equation. We use Darboux transformation to construct simultaneously exact solutions Lax system associated with breathers. obtain a full description spectra for two breathers, including multiplicities eigenvalues. Solutions linearized NLS equ...