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I want to comparison between oscillons based on non-linearities. Can someone elaborate it with the reason behind it :

When the sinusoidal vibrations are of the correct amplitude and frequency and the layer of sufficient thickness, a localized wave, referred to as an oscillon.

Astonishingly, oscillons of opposite phase will attract over short distances and form 'bonded' pairs. Oscillons of like phase repel. Oscillons have been observed forming 'molecule' like structures and long chains. In comparison, solitons do not form bound states.

Reference: Wiki

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Oscillons and solitons are two specific types of nonlinear waves. Solitons are considered to be nonlinear partly because their phase speed depends upon amplitude and their spatial scale. I think the main differences between the two are that oscillons are solutions in granular media, they can change form when colliding with other oscillons, and oscillons can be stationary waves. Generally speaking, solitons are solutions to KdV(Korteweg-de Vries)-like equations.

G.B. Whitham has a book that goes into gory detail regarding nonlinear waves and solutions to KdV-like equations (many solutions are solitons).

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