page_title: Peregrine soliton
section_title: In the spatio-temporal domain
hierarchical_section_title: Peregrine soliton / Mathematical expression / In the spatio-temporal domain
caption_attribution_description: Français&#160;: Profils temporel et spectral au point de compression maximal d'un soliton de Peregrine
context_page_description: The Peregrine soliton is an analytic solution of the nonlinear Schrödinger equation. This solution was proposed in 1983 by Howell Peregrine, researcher at the mathematics department of the University of Bristol.
context_section_description: The Peregrine soliton is a solution of the one-dimensional nonlinear Schrödinger equation that can be written in normalized units as follows :
  with  the spatial coordinate and  the temporal coordinate.  being the envelope of a surface wave in deep water. The dispersion is anomalous and the nonlinearity is self-focusing (note that similar results could be obtained for a normally dispersive medium combined with a defocusing nonlinearity).
  The Peregrine analytical expression is:
  so that the temporal and spatial maxima are obtained for  and .
caption: Spatial and temporal profiles of a Peregrine soliton obtained at the point of maximum compression
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