• J. T. Mendonça
  • Hugo Terças
Part of the Springer Series on Atomic, Optical, and Plasma Physics book series (SSAOPP, volume 70)


In this chapter, we discuss the main properties of the solitary structures in Bose-Einstein condensates. As we are about to see, they occur as a natural consequence of the description of the condensate, at the mean-field level, in terms of the Gross-Pitaevskii equation, which is nonlinear in the condensate wave function ϕ. In general terms, a soliton is an “envelope”, very often being bell-shaped, which propagates with very little dispersion. They usually arise as a unique solution of a widespread class of nonlinear field equations, where the effects of the dispersion balance with the nonlinearity of the system. According to the accepted historical facts, the soliton phenomenon was first observed by by John Scott Russell, who observed a solitary wave in the Union Canal in Scotland. He reproduced the phenomenon in a wave tank and named it the “wave of translation” [1].


Solitary Wave Soliton Solution Dark Soliton Bright Soliton Harmonic Trap 
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Copyright information

© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  • J. T. Mendonça
    • 1
  • Hugo Terças
    • 2
  1. 1.Instituto Superior TecnicoLisbonPortugal
  2. 2.Université Blaise PascalAubière CedexFrance

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