Magnetic waves in an ultracold gas behave like elastic cords. Two or three such cords can twist into a single knot that breathes: it contracts and expands, but never unravels. For the first time, scientists assembled such knots in the lab and confirmed that their breathing matches calculations exactly.

The gas consisted of two atomic species that do not mix, like oil and water. The magnetic properties of this gas are described by an equation similar to the one for waves on a rope. This equation has special solutions — solitons, solitary waves that do not spread out. From them, one can build composite states resembling a bundle of several ropes.

A weak point-like perturbation on such a knot destroys its integrity. The knot breaks into individual cords — fundamental solitons. This decay is like a reverse mathematical operation: recovering simple components from a complex wave. The experiment showed that composite magnetic solitons are real, and they can be created and disassembled piece by piece.