SciPost Submission Page
NonlinearSchrodinger: Higher-Order Algorithms and Darboux Transformations for Nonlinear Schrödinger Equations
by Omar A. Ashour
Submission summary
| As Contributors: | Omar Ashour |
| Preprint link: | scipost_202103_00007v1 |
| Code repository: | https://github.com/oashour/NonlinearSchrodinger.jl |
| Date submitted: | 2021-03-04 20:36 |
| Submitted by: | Ashour, Omar |
| Submitted to: | SciPost Physics Codebases |
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
NonlinearSchrodinger.jl is a Julia package with a simple interface for studying solutions of nonlinear Schrödinger 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-Nyström 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.
Current status:
Editor-in-charge assigned