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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:
  • Mathematical Physics
  • Mathematical Software
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:
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Submission scipost_202103_00007v1 on 4 March 2021

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