WIAS Preprint No. 2276, (2016)

Adiabatic theory of champion solitons


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

2010 Mathematics Subject Classification

  • 78A60 35Q60 70H11

2010 Physics and Astronomy Classification Scheme

  • 42.65.-k, 42.81.Dp, 05.45.Yv, 03.65.Nk


  • Champion solitons, All-optical switching, Extreme events, Soliton perturbation theory, Event horizons




We consider scattering of small-amplitude dispersive waves at an intense optical soliton which constitutes a nonlinear perturbation of the refractive index. Specifically, we consider a single-mode optical fiber and a group velocity matched pair: an optical soliton and a nearly perfectly reflected dispersive wave, a fiber-optical analogue of the event horizon. By combining (i) an adiabatic approach that is used in soliton perturbation theory and (ii) scattering theory from Quantum Mechanics, we give a quantitative account for the evolution of all soliton parameters. In particular, we quantify the increase in the soliton peak power that may result in spontaneous appearance of an extremely large, so-called champion soliton. The presented adiabatic theory agrees well with the numerical solutions of the pulse propagation equation. Moreover, for the first time we predict the full frequency band of the scattered dispersive waves and explain an emerging caustic structure in the space-time domain.

Appeared in

  • Phys. Rev. A, 94 (2016) pp. 033811/1--033811/12.

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