WIAS Preprint No. 1639, (2011)

Dispersion of nonlinear group velocity determines shortest envelope solitons


  • Amiranashvili, Shalva
    ORCID: 0000-0002-8132-882X
  • Bandelow, Uwe
    ORCID: 0000-0003-3677-2347
  • Akhmediev, Nail

2008 Physics and Astronomy Classification Scheme

  • 42.65.Tg 05.45.Yv 42.81.Dp


  • Generalized nonlinear Schrödinger equation, Nonlinear group velocity dispersion, Soliton, Cusp




We demonstrate that a generalized nonlinear Schrödinger equation (NSE), that includes dispersion of the intensity-dependent group velocity, allows for exact solitary solutions. In the limit of a long pulse duration, these solutions naturally converge to a fundamental soliton of the standard NSE. In particular, the peak pulse intensity times squared pulse duration is constant. For short durations this scaling gets violated and a cusp of the envelope may be formed. The limiting singular solution determines then the shortest possible pulse duration and the largest possible peak power. We obtain these parameters explicitly in terms of the parameters of the generalized NSE.

Appeared in

  • Phys. Rev. A, 84 (2011) pp. 43834/1--043834/5

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