Related papers: A new approach to the absorbing boundary condition…
Based on the work of Nuttall and Cohen [Phys. Rev. {\bf 188} (1969) 1542] and Resigno et al{} [Phys. Rev. A {\bf 55} (1997) 4253] we present a rigorous formalism for solving the scattering problem for long-range interactions without using…
In this paper, we shall study the boundary case for complex Monge-Amp\`ere type equations under certain geometric assumptions.
We consider a number of linear and non-linear boundary value problems involving generalized Schr\"odinger equations. The model case is $-\Delta u=Vu$ for $u\in W_0^{1,2}(D)$ with $D$ a bounded domain in ${\bf R^n}$. We use the Sobolev…
One-dimensional time-independent Schr\"odinger equation is solved for the asymmetric Hulth\'{e}n potential. Reflection and transmission coefficients and bound state solutions are obtained in terms of the hypergeometric functions. It is…
A first-principle multiscale modeling approach is presented, which is derived from the solution of the Ornstein-Zernike equation for the coarse-grained representation of polymer liquids. The approach is analytical, and for this reason is…
In this paper, we introduce some new ideas to study Schrodinger equations in RN with power-type nonlinearities.
We present some a - priori bounds from above and from below for solutions to a class of conformally invariant Schroedinger equations. As a by - product we deduce some new uniqueness results.
The integrating factor technique is widely used to solve numerically (in particular) the Schr\"odinger equation in the context of spectral methods. Here, we present an improvement of this method exploiting the freedom provided by the gauge…
In the present paper we introduce a new methodology for the construction of numerical methods for the approximate solution of the one-dimensional Schr\"odinger equation. The new methodology is based on the requirement of vanishing the…
We find infinitely many positive non-radial solutions for a system of Schr\"odinger equations with critical growth in a fully attractive or repulsive regime in presence of an external radial trapping potential.
In contrast with classical Schwarz theory, recent results have shown that for special domain geometries, one-level Schwarz methods can be scalable. This property has been proved for the Laplace equation and external Dirichlet boundary…
This paper presents an integral formulation for Helmholtz problems with mixed boundary conditions. Unlike most integral equation techniques for mixed boundary value problems, the proposed method uses a global boundary charge density. As a…
The matrix Schr\"odinger equation is considered on the half line with the general selfadjoint boundary condition at the origin described by two boundary matrices satisfying certain appropriate conditions. It is assumed that the matrix…
Half-space boundary Kramers' problem about isothermal sliding of moderate dense gas with accomodation boundary conditions along a flat firm surface is solving. The new method of the solution of boundary problems of the kinetic theory is…
Multifluid simulations of plasma sheaths are increasingly used to model a wide variety of problems in plasma physics ranging from global magnetospheric flows around celestial bodies to plasma-wall interactions in thrusters and fusion…
In this paper, via applying the method developed by A. Cianchi and V. Maz'ya, the author obtains the global boundedness of the gradient for solutions to Dirichlet and Neumann problems of a class of Schr\"odinger equations under the minimal…
We present a constructive method to devise boundary conditions for solutions of second-order elliptic equations so that these solutions satisfy specific qualitative properties such as: (i) the norm of the gradient of one solution is bounded…
We prove the existence of a new type of solutions to a nonlinear Schr\"odinger system. These solutions, which we call "multi-speeds solitary waves", are behaving at large time as a couple of scalar solitary waves traveling at different…
We apply the spectral element method to the determination of scattering and bound states of the multichannel Schr\"odinger equation. In our approach the reaction coordinate is discretized on a grid of points whereas the internal coordinates…
We consider the study of a numerical scheme for an initial- and Dirichlet boundary- value problem for a nonlinear Schr\"odinger equation. We approximate the solution using a, local (non-uniform) two level scheme in time (see C. Besse [6]…