Global InformationSchamel equation information
The Schamel equation (S-equation) is a nonlinear partial differential equation of first order in time and third order in space. Similar to a Korteweg–De Vries equation (KdV),[1] it describes the development of a localized, coherent wave structure that propagates in a nonlinear dispersive medium. It was first derived in 1973 by Hans Schamel [2] to describe the effects of electron trapping in the trough of the potential of a solitary electrostatic wave structure travelling with ion acoustic speed in a two-component plasma. It now applies to various localized pulse dynamics such as:
- electron and ion holes or phase space vortices in collision-free plasmas such as space plasmas,[3]
- axisymmetric pulse propagation in physically stiffened nonlinear cylindrical shells,[4]
- "Soliton" propagation in nonlinear transmission lines [5] or in fiber optics and laser physics.[6]
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