[danwills]

Indeed! I rather like the idea that solitons are something like the simplest self-propagating 'things' in any medium/computation-reigeme, so gliders in Game-of-Life might qualify and in more complex/subtle systems they can have more complex behaviours as well (like bacteria, or flies? Hehe) Here's a fun example I made in gollygang/Ready (and Houdini) of PDE solitons that spin around with rippling wakes:

https://youtu.be/edNG2EJWQwQ?si=8b3YsHCDIaj0C7Pa

[ryanartecona]

Wow! I'd never heard of gollygang/ready before, but it looks extremely cool. Thanks for sharing.

[danwills]

No probs, I've had a great deal of fun playing with it indeed! Hope you do too!

[pcthrowaway]

Would sound waves then count as solitons?

[IAmBroom]

Only if they retain their original shape. The point is not that any wave is a soliton, but a soliton never changes shape as it moves (through time, a medium, or whatever). The soliton can decrease in amplitude, and expand in width, but otherwise remains the same.

A pure, single Gaussian hump is the soliton for homogenous linear media. If you create an audible with the spectral shape of a Gaussian (and therefore also the time shape), it might get quieter as it moves across the room, and longer, but will still "sound" the same.

[danwills]

I believe so, although the way I usually think about Solitons is like a single packet.. so just one cycle of a wave. Continuous sound could probably be thought of as a continuous stream of solitons (I think ppl call them phonons when it's sound though). I haven't studied PDEs nor solitons in a formal way I just love playing with them. Gray Scott with History and Wave (a formula I contributed to Gollygang/Ready) supports many fascinating soliton behaviours. Here's 25mins of one of the strangest parameter settings I've found:

https://youtu.be/Naj_J8aznyk?si=Da3A3iTz8rN9qrgq