This paper addresses the theoretical analysis of a fully discrete scheme for the one-
dimensional time-dependent Schrödinger equation on unbounded domain. We first reduce …

This paper addresses the finite element method for the two-dimensional time-dependent
Schrödinger equation on an infinite strip by using artificial boundary conditions. We first …

In this paper, we construct semi-discrete two-grid finite element schemes and full-discrete
two-grid finite element schemes for the two-dimensional time-dependent Schrödinger …

Spectral Collocation Solutions to Problems on Unbounded Domains Page 1 Spectral
Collocation Solutions to Problems on Unbounded Domains Calin-Ioan Gheorghiu …

This paper presents an automatic algorithm for detecting and generating solitary waves of
nonlinear wave equations. With this purpose, dynamic simulations are carried out, the …

This paper presents some numerical methods to simulate the evolution of coherent
structures with small fluctuations, that appear as typical solutions of a class of nonintegrable …

This paper presents error analysis of hybridizable discontinuous Galerkin (HDG)
timedomain method for solving time dependent Schrödinger equations. The numerical trace …

We introduce a practical algorithm to automate the simulations of solitary wave solutions of
some nonlinear dispersive wave equations. The full discretization consists of a spatial …

The purpose of this work is to determine suitable numerical methods to simulate the
evolution of coherent structures for the cubic nonlinear Schrödinger equation with Dirichlet …

Estudiamos métodos numéricos para simular la evolución de ground states en un fondo de
turbulencias, modeladas por ecuaciones de tipo Schrödinger no lineal. Los métodos están …