nLab soliton

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Context

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Contents

Idea

The term soliton originates as an abbreviation of “solitary wave”, in the tradition of naming fields and particles ending on “-on”.

A soliton solution of a nonlinear wave equation is a solution whose large amplitude part is localized in space and is asymptotically stable in time. This asymptotic stability (more precisely non-damping and asymptotic preservation of shape, up to translation) is typically a feature of an infinite number of conservation laws, and many models of equations allowing soliton solutions are in fact integrable systems (with infinitely many degrees of freedom). Soliton solution often combine to multisoliton solutions in a nonlinear way, with a period of interaction when they “meet”, but after a passage of some time, the waves gradually uncouple and regain their original shape when outgoing to infinity. A typical example of a nonlinear wave equation exhibiting soliton solutions is the exactly solvable “nonlinear Schroedinger equation” appearing in optics.

Solitons appear in description of many natural phenomena. For example, Davydov soliton (wikipedia) has a role in stabilizing dynamics of proteins.

Examples

Refereneces

(See also the general references at non-perturbative quantum field theory.)

In the context of hadrodynamics (Skyrmions):

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