oashour / nonlinearschrodinger.jl Goto Github PK

A suite of tools for solving Nonlinear Schrodinger equations via higher-order algorithms and Darboux transformations.

License: MIT License

Julia 100.00%

nonlinear-dynamics nlse mathematical-physics nonlinear-optics nonlinear-schrodinger julia darboux-transformation

nonlinearschrodinger.jl's Introduction

NonlinearSchrodinger.jl

NonlinearSchrodinger.jl is a suite of tools for studying Nonlinear Schrodinger equations. The purpose of this package is to encourage the use of open source software in studying these equations as most works in this field rely on closed-source codes. This allows for reproducability, lowers the barrier for new researchers, and alleviates the need to reinvent the wheel.

Features

Solving the cubic Nonlinear Schrodinger equation using a plethora of algortithms of order up to 8 (the number of algorithms available is always increasing!). Symplectic and RKN integrators are available.
Solving the Hirota and Sasa-Satsuma equations using a combined split-step-finite-difference approach using a few different integrators. This is a preliminary feature and is not yet fully supported.
Computing the integrals of motion (energy, momentum, and particle number) and their errors.
Computing the Darboux Transformation to study complicated analytical solutions. We currently support the breather and soliton seeds for extended nonlinear Schrodinger equations of order up to 5 (including cubic NLS, Hirota, LPD, Quintic, and arbitrary combinations thereof). We also support the cn and dn seeds for the cubic NLS.
Easy visualization through Plots.jl recipes.
A very simple interface that allows one to compute very complicated solutions via only a few lines of code.
Many utilities for studying maximal intensity breather families on uniform and dnoidal backgrounds, pruning for Nonlinear talbot carpets, and breather to soliton conversion in extended NLSEs.

Example: 7 Soliton Collision

xᵣ = -10=>10
T = 20
seed = "0"
box = Box(xᵣ, T, Nₓ=500, Nₜ = 500)
λ = [-0.45 + 0.775im, -0.35 + 0.8im, -0.25 + 0.825im, 0.85im, 0.25 + 0.875im, 0.35 + 0.9im, 0.45 + 0.925im]
xₛ = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
tₛ = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]

calc = Calc(λ, tₛ, xₛ, seed, box)

solve!(calc)
heatmap(calc)

Supporting and Citing

The paper can be found here. It is currently under review.

Logo

The logo is formed by 3 Akhmediev breathers with a = 3/8, an homage to my first paper in the field.

nonlinearschrodinger.jl's People

Contributors

Stargazers

Watchers

Forkers

sailfish009 nature-science-computing juliatagbot arunkv7 kuantumbs

nonlinearschrodinger.jl's Issues

Axis labels are too close to ticks

Plots from plot_IoM show up very slowly

This is likely due to the fact that they have very small differences in numbers which might be causing issues with either GR or Plots.jl. I am not sure what the fix is but this is worth looking into. There is some fuzziness in the lines themselves, indicating some numerical noise.

Switching to the plot in the VSCode plot pane is also extremely slow.

Memory optimization: save only when needed

Similar to the save_at flag from DifferentialEquations.jl

compute_spectrum very slow

compute_spectrum which computes the FFT and FFTshifts is very slow. For calculations with lower order integrators and small number of Fourier nodes, compute_spectrum often takes twice as long as the simulation itself. Enabling multi threading for FFTW before computing this FFT improves performance by a factor of 2, but I am not sure if there is much to be done about it. The best option might be to compete the FFT somehow during the main solver loop itself, this is likely a better option than doing the whole thing at once later on.

Public and private types and functions are a mess

Modules are currently a little messy, as well as the exports. This needs to be cleaned up before starting work on the Darboux section of the package.

Documentation does not deploy

The documentation compiles fine and looks good locally, but is not deployed on github and no gh_pages branch is created.

TagBot trigger issue

This issue is used to trigger TagBot; feel free to unsubscribe.

If you haven't already, you should update your TagBot.yml to include issue comment triggers.
Please see this post on Discourse for instructions and more details.

If you'd like for me to do this for you, comment TagBot fix on this issue.
I'll open a PR within a few hours, please be patient!

Helper functions for DT+Simulation

A function to calculate the maximal intensity family given lambda or m. It should return an array of eigenvalues, as well as the relevant shift arrays (maybe, just zeros basically).
Function to generate DT based initial condition for simulations
Function to generate DT based cosine-series initial condition for simulations

Helper functions for DT

Helper functions and utilities/QoL changes should include:

A way to set the number of x nodes directly in Box, instead of being forced to set dx, which doesn't make too much sense for DT.
Extend the function compute_params to compute all the relevant parameters as currently done in the constructor of calc. This will add modularity and make life easier for other functions.

Move to abstract types

Currently the code is poorly written in a way that uses Float64 or Complex{Float64}. This should be changed to use abstract types. This happens in both function arguments as well as when allocating arrays such as in init_sim.