NonlinearSchrodinger: Higher-Order Algorithms and Darboux Transformations for Nonlinear Schr\"odinger Equations
Computational Physics
2021-03-29 v1 Mathematical Software
Numerical Analysis
Numerical Analysis
Exactly Solvable and Integrable Systems
Abstract
NonlinearSchrodinger.jl is a Julia package with a simple interface for studying solutions of nonlinear Schr\"odinger equations (NLSEs). In approximately ten lines of code, one can perform a simulation of the cubic NLSE using one of 32 algorithms, including symplectic and Runge-Kutta-Nystr\"om integrators up to eighth order. Furthermore, it is possible to compute analytical solutions via a numerical implementation of the Darboux transformation for extended NLSEs up to fifth order, with an equally simple interface. In what follows, we review the fundamentals of solving this class of equations numerically and analytically, discuss the implementation, and provide several examples.
Cite
@article{arxiv.2103.14469,
title = {NonlinearSchrodinger: Higher-Order Algorithms and Darboux Transformations for Nonlinear Schr\"odinger Equations},
author = {Omar A. Ashour},
journal= {arXiv preprint arXiv:2103.14469},
year = {2021}
}
Comments
43 pages, 15 figures. Submitted to Scipost Physics Codebases