Split-step methods for the solution of the nonlinear Schro¨dinger equation
SIAM Journal on Numerical Analysis
Numerical simulation of nonlinear Schro¨dinger systems: a new conservative scheme
Applied Mathematics and Computation
On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
Journal of Computational Physics
Journal of Computational Physics
A Relaxation Scheme for the Nonlinear Schrödinger Equation
SIAM Journal on Numerical Analysis
Journal of Computational Physics
A perfectly matched layer approach to the nonlinear Schrödinger wave equations
Journal of Computational Physics
Journal of Computational Physics
Numerical solution to coupled nonlinear Schrödinger equations on unbounded domains
Mathematics and Computers in Simulation
Simulation of coherent structures in nonlinear Schrödinger-type equations
Journal of Computational Physics
Adaptive artificial boundary condition for the two-level Schrödinger equation with conical crossings
Journal of Computational Physics
Journal of Computational Physics
Computational Solution of Blow-Up Problems for Semilinear Parabolic PDEs on Unbounded Domains
SIAM Journal on Scientific Computing
Numerical Blow-up of Semilinear Parabolic PDEs on Unbounded Domains in R2
Journal of Scientific Computing
Absorbing Boundary Conditions for General Nonlinear Schrödinger Equations
SIAM Journal on Scientific Computing
Discrete artificial boundary conditions for nonlinear Schrödinger equations
Mathematical and Computer Modelling: An International Journal
Journal of Computational Physics
Hi-index | 31.48 |
The numerical approximation of one-dimensional cubic nonlinear Schrödinger equations on the whole real axis is studied in this paper. Based on the work of A. Boutet de Monvel, A.S. Fokas and D. Shepelsky [Lett. Math. Phys., 65(3): 199-212, 2003], a kind of exact nonreflecting boundary conditions are derived on the artificially introduced boundary points. The related numerical issues are discussed in detail. Several numerical tests are performed to demonstrate the behaviour of the proposed scheme.