Solitons1D

A Julia package to compute 1D soliton dynamics.

This package is being developed by Víctor Díaz Díaz as part of the Ph.D. thesis Rigorous and analytical approximation methods in soliton theories.

Installation

This package is not registered in the Julia General Registry (yet).

To install this package, clone this repository:

git clone https://github.com/vddiazz/Solitons1D.jl

Then move into the repository folder and run Julia. In the REPL do:

using Pkg
Pkg.activate(".")
Pkg.instantiate()

Features

This package is aimed at computing kink-antikink (KAK) collisions using full-field (FF) dynamics and collective coordinate models (CCM).

Full Field (FF):

• KAK collisions for $\phi^4$ theory on $\mathbb{R}$.
• KAK-KAK collisions for $\phi^4$ theory on $S^1$.

Collective Coordinate Models (CCM):

• KAK moduli space dynamics for Poincaré mode + shape mode.
• KAK moduli space dynamics for Poincaré mode + modified shape mode.

References

[1] Manton N., Sutcliffe P. (2004), Topological Solitons, Cambridge University Press.

[2] Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P. (2007), Numerical Recipes: The Art of Scientific Computing (3º ed.), Cambridge University Press.