NonlinearSchrodinger

A suite of tools for Nonlinear Schrodinger Equations

NonlinearSchrodinger.jl is a suite of tools for solving Nonlinear Schrodinger equations via higher-order algorithms and Darboux transformations.

Package Features

The following features are currently available:

• 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 Nystrom integrators are available.
• Solving the Hirota and Sasa-Satsuma equations using a combined split-step-finite-difference approach using a few different integrators.
• 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.
• Very simple API that allows one to compute very complicated solutions via only a few lines of code.

Examples

• Darboux Transformation Examples
• Example 1: 7 Soliton Collision
• Example 2: Fifth Order Maximal Intensity Breather
• Example 3: 3 Soliton Collision on a $cn$ background
• Example 4: First Order Breather matched to a $dn$ Background

• Simulation Examples
• Example 1: Cosine Wave Initial Condition
• Example 2: Soliton Initial Condition
• Example 3: Nonlinear Talbot Carpet (Pruning)
• Example 4: Darboux Transformation Initial Condition

Index

• NonlinearSchrodinger.Box
• NonlinearSchrodinger.Calc
• NonlinearSchrodinger.Sim
• NonlinearSchrodinger.PHF
• NonlinearSchrodinger.compute_IoM!
• NonlinearSchrodinger.params
• NonlinearSchrodinger.solve!
• NonlinearSchrodinger.solve!
• NonlinearSchrodinger.λ_given_f
• NonlinearSchrodinger.λ_given_m
• NonlinearSchrodinger.λ_maximal
• NonlinearSchrodinger.ψ₀_DT
• NonlinearSchrodinger.ψ₀_periodic