This repository includes all code and data which is used for the manuscript of the same name (https://doi.org/10.1103/ths6-1wgp, https://arxiv.org/abs/2503.04560). It is written in a Jupyter notebook in Julia 1.11.1. The Jupyter notebook "Nonlinear-Eliashberg-theory" is the main file, it uses the functions "T_crit.jl", "Im_bandgap.jl", "Re_bandgap.jl", "Re_bandgap_fast.jl", and "Re_bandgap_0K.jl". All SVG files are in the 'Figures' folder, and are the figures which are already generated and used in the manuscript. The files without .domain (T_c, Im_sol, Re_sol, ...) in the 'Data' folder are the raw data which is generated by the code, and which is used for the figures of the manuscript. Explanation of the notebook is written in the notebook itself. For further questions you can email me.