Accessible solitons

Solitons are ubiquitous, Their description involves abstruse mathematics and is limited to a two-dimensional idealization. A nonlocal model is presented that provides a radical simplification and allows for an elegant description of soliton collisions, interactions, and deformations in two and three dimensions. The model reveals an intimate connection between solitons and the linear harmonic oscillator. It foreshadows a photonic switch in which a bright beam can steer a distant dim beam, and it predicts the existence of noncircularly symmetric solitons.