The exciting new results surrounding the Higgs field have led to physics conversations about interactions between solitons, or nonlinear standing waves that can maintain their characteristics after colliding. Higgs field interactions results in mass, and QFT uses solitons. So people with mathematical and computational interests in physics are looking at soliton models.
The Kadomtsev-Petviashvili Equation is an equation that models the behavior of nonlinear wave motion. This includes nonlinear static waves, as can emerge in as shallow water, but it has applications across other states of matter.
It is more known now in Mathematical Physics and String Theory communities for its applications to other states of matter and areas of active research like ferromagnetism and para(ferro)magnetism. It describes the behavior of mass waves in Bose-Einstein condensates, too.
The Higgs field gives rise to mass in a way that's similar to non-Abelian Lie groups over connected topologies. Rotations in higher dimension spaces are modeled easily using non-Abelian Lie algebras and the qualities defines a Lie algebra equation are mostly present in the Kadomtsev-Petviashvili Equation, making it a Lie group for all connected toplogies.
This Python 3 script builds on an implementation of the Kadomtsev-Petviashvili Equation using a Fast Fourier Transform and the Burgers Equation to simplify its implientation.
For example, it can model rare phenomena seen in standing waves and solitons. A surface tension parameter can be added.
It is also used to model standing wave / soliton type phenomena in other phases of matter like matter waves Bose-Einstein condensates. Ferromagnetism also exhibits this type of standing wave phenomenon.
More reading:
https://en.wikipedia.org/wiki/Kadomtsev%E2%80%93Petviashvili_equation https://en.wikipedia.org/wiki/Dispersionless_equation#Dispersionless_KP_equation
https://mathworld.wolfram.com/Kadomtsev-PetviashviliEquation.html https://mathworld.wolfram.com/Kadomtsev-Petviashvili-BurgersEquation.html
Draws on source code by George Meshveliani here: https://github.com/George1Meshveliani/Kadomtsev-Petviashvili-Equation
In the source code, try changing the value of nu by very small values or modulating an infintesimal.
At some point this would be nice to see animated.