相关论文: Exact transparent boundary condition for the multi…

We show that some boundary conditions assumed at a thin membrane may result in normal diffusion not being the stochastic Markov process. We consider boundary conditions defined in terms of the Laplace transform in which there is a linear…

The Schr\"{o}dinger equation, in hyperspherical coordinates, is solved in closed form for a system of three particles on a line, interacting via pair delta functions. This is for the case of equal masses and potential strengths. The…

On the contrary to the common intuition, which suggests that a steep expulsive potential makes quantum states widely delocalized, we demonstrate that one- and two-dimensional (1D and 2D) Schroedinger equations, which include expulsive…

Achieving exact unidirectional invisibility in a finite frequency band has been an outstanding problem for many years. We offer a simple solution to this problem in two dimensions that is based on our solution to another more basic open…

Bound states in the continuum (BICs), with the ability of trapping and manipulating waves within the radiation continuum, have gained significant attention for their potential applications in optics and acoustics. However, challenges arise…

Many nanostructures today are low-dimensional and flimsy, and therefore get easily distorted. Distortion-induced symmetry-breaking makes conventional, translation-periodic simulations invalid, which has triggered developments for new…

Quasi-Exactly Solvable Schr\"odinger Equations occupy an intermediate place between exactly-solvable (e.g. the harmonic oscillator and Coulomb problems etc) and non-solvable ones. Their major property is an explicit knowledge of several…

We present a barrier potential with bound states that is exactly solvable and determine the eigenfunctions and eigenvalues of the Hamiltonian. The equilibrium density matrix of a particle moving at temperature T in this nonlinear barrier…

Differential equations need boundary conditions (BC's) for their solution. It is commonly acknowledged that differential equations and BC's are representative of independent physical processes, and no correlations between them is required.…

Under investigation in this work is the inverse scattering transform of the general fifth-order nonlinear Schr\"{o}dinger equation with nonzero boundary conditions (NZBCs), which can be reduced to several integrable equations. Firstly, a…

In this paper, we introduce artificial boundary conditions for the linearized Green-Naghdi system of equations. The derivation of such continuous (respectively discrete) boundary conditions include the inversion of Laplace transform…

The three-dimensional (3D) full compressible magnetohydrodynamic system is studied in a general bounded domain with slip boundary condition for the velocity filed, adiabatic condition for the temperature and perfect conduction for the…

We present an efficient method for propagating the time-dependent Kohn-Sham equations in free space, based on the recently introduced Fourier contour deformation (FCD) approach. For potentials which are constant outside a bounded domain,…

Many-particle systems pose commonly known computational challenges in quantum theory. The obstacles arise from the difficulty in finding sets of eigenvalues and eigenvectors of the underlying Hamiltonian while enforcing fermion or boson…

We consider the numerical integration of Langevin equations for particles in a channel, in the presence of boundary conditions fixing the concentration values at the ends. This kind of boundary condition appears for instance when…

The 3D incompressible Euler equations in a bounded domain are most often supplemented with impermeable boundary conditions, which constrain the fluid to neither enter nor leave the domain. We establish well-posedness with inflow, outflow of…

In this work we consider the free boundary inverse equilibrium problem for 3D ideal MHD. We review boundary conditions for both fixed and free boundary solutions and under what circumstances a sheet current may exist at the plasma-vacuum…

This paper reports several new classes of weakly unstable recurrent solutions of the 2+1-dimensional Euler equation on a square domain with periodic boundary conditions. These solutions have a number of remarkable properties which…

We introduce a new exactly integrable potential for the Schr\"odinger equation for which the solution of the problem may be expressed in terms of the Gauss hypergeometric functions. This is a potential step with variable height and…

Solving numerically hydrodynamical problems of incompressible fluids raises the question of handling first order derivatives (those of pressure) in a closed container and determining its boundary conditions. We research several pressure…