Solitons

The Korteweg-de Vries, nonlinear Schrodinger, and Sine-Gordon equations: shape-preserving traveling waves, elastic collisions, wavepacket spreading, and topologically protected kinks – several animated frame by frame.

An elastic KdV soliton-soliton collision

An elastic KdV soliton-soliton collision

Zabusky-Kruskal fission: coining “soliton”

Zabusky-Kruskal fission: coining "soliton"

Russell’s wave of translation

Russell's wave of translation

A dispersion-free optical soliton

A dispersion-free optical soliton

Schrodinger’s wavepacket spreading

Schrodinger's wavepacket spreading

A topologically protected Sine-Gordon kink

A topologically protected Sine-Gordon kink

An exact kink-antikink collision from inverse scattering

An exact kink-antikink collision from inverse scattering