An Introduction to Solitons and Oscillons

Noah Graham

Physics Department, Middlebury College

Ordinary waves, like a musical note, the beam of a flashlight, or ripples on a pond, tend to disperse. We can understand this behavior by breaking the wave into its Fourier components, each with a definite wavelength, frequency and direction of propagation. By plucking a string, turning on a light, or dropping a rock in a pond, one typically creates a superposition of many such waves, each of which propagates independently, leading to dispersion. In the Standard Model of particle physics, however, there appear nonlinear effects through which waves can interact, rather than simply passing through each other and dispersing. This modification opens up the possibility of waves forming coherent lumps that do not disperse. These objects can take the form of static configurations, called solitons, and configurations that undergo regular oscillations, called oscillons or breathers. Such objects could be of particular interest in the early universe, when the higher energies available can facilitate their formation.

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