Asymptotics of odd solutions for cubic nonlinear Schrödinger equations

Artificial boundary conditions for one-dimensional cubic nonlinear Schrödinger equations

This paper addresses the construction of nonlinear integro-differential artificial boundary conditions for one-dimensional nonlinear cubic Schrödinger equations. Several ways of designing such conditions are provided and a theoretical classification of their accuracy is given. Semi-discrete time schemes based on the method developed by Durán and Sanz-Serna [IMA J. Numer. Anal. 20 (2) (2000), pp...

On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations

We give an error analysis of Strang-type splitting integrators for nonlinear Schrödinger equations. For Schrödinger-Poisson equations with an H4-regular solution, a first-order error bound in the H1 norm is shown and used to derive a second-order error bound in the L2 norm. For the cubic Schrödinger equation with an H4-regular solution, first-order convergence in the H2 norm is used to obtain s...

Of Nonlinear Schrödinger Equations

The authors suggest a new powerful tool for solving group classification problems, that is applied to obtaining the complete group classification in the class of nonlinear Schrödinger equations of the form iψt +∆ψ + F (ψ,ψ ∗) = 0.

Existence of infinitely many solutions for coupled system of Schrödinger-Maxwell's equations

A spatial sixth-order alternating direction implicit method for two-dimensional cubic nonlinear Schrödinger equations

Based on the combined compact difference scheme, an alternating direction implicit method is proposed for solving two-dimensional cubic nonlinear Schrödinger equations. The proposed method is sixth-order accurate in space and second-order accurate in time. The linear Fourier analysis method is exploited to study the stability of the proposed method. The efficiency and accuracy of the proposed m...