非线性薛定谔方程分裂吸收边界条件的统一方法

Exact splitting methods for kinetic and Schr{ö}dinger equations

In [8], some exact splittings are proposed for inhomogeneous quadratic differential equations including, for example, transport equations, kinetic equations, and Schr{ö}dinger type equations with a rotation term. In this work, these exact splittings are combined with pseudo-spectral methods in space to illustrate their high accuracy and efficiency.

Sobolev范数的增长与离散非线性Schrödinger方程的强收敛

Growth of Sobolev norms and strong convergence for the discrete nonlinear Schr{ö}dinger equation

本文证明了无限格上离散非线性Schrödinger方程的解在任意Sobolev范数下强收敛于全空间连续方程的解，核心方法依赖Shannon插值的双线性估计与离散Sobolev范数增长控制。

On a nonlinear Schr{ö}dinger equation for nucleons in one space dimension

We study a 1D nonlinear Schr{ö}dinger equation appearing in the description of a particle inside an atomic nucleus. For various nonlinearities, the ground states are discussed and given in explicit form. Their stability is studied numerically via the time evolution of perturbed ground states. In the time evolution of general localized initial data, they are shown to appear in the long time behaviour of certain cases.

Analysis of the Feshbach-Schur method for the Fourier Spectral discretizations of Schr{ö}dinger operators

In this article, we propose a new numerical method and its analysis to solve eigenvalue problems for self-adjoint Schr{ö}dinger operators, by combining the Feshbach-Schur perturbation theory with the spectral Fourier discretization. In order to analyze the method, we establish an abstract framework of Feshbach-Schur perturbation theory with minimal regularity assumptions on the potential that is then applied to the setting of the new spectral Fourier discretization method. Finally, we present some numerical results that underline the theoretical findings.

具解析势的线性与非线性周期Schrödinger方程的先验误差分析

A priori error analysis of linear and nonlinear periodic Schr{ö}dinger equations with analytic potentials

该文针对具解析势的线性与非线性周期Schrödinger方程开展先验误差分析，明确非线性情形下势的正则性不再自动传递给解，并研究了平面波（Fourier）离散化方法的收敛速率。

非线性薛定谔方程激发态的计算：数值与理论分析

Computation of excited states for the nonlinear Schr{ö}dinger equation: numerical and theoretical analysis

本文提出基于Nehari流形的新方法计算径向非线性薛定谔方程激发态，与打靶法比较，该方法在大区域上更精确但速度较慢。