WIAS Preprint No. 1696, (2012)

Persistence of rogue waves in extended nonlinear Schrödinger equations: Integrable Sasa--Satsuma case



Authors

  • Bandelow, Uwe
    ORCID: 0000-0003-3677-2347
  • Akhmediev, Nail

2010 Mathematics Subject Classification

  • 35Q55 35Q60 37K40

2008 Physics and Astronomy Classification Scheme

  • 42.65.Tg 05.45.Yv 42.81.Dp

Keywords

  • Generalized nonlinear Schrödinger equations, Sasa-Satsuma equation, solitons, rogue waves

Abstract

We present the lowest order rogue wave solution of the Sasa-Satsuma equation (SSE) which is one of the integrable extensions of the nonlinear Schrödinger equation (NLSE). In contrast to the Peregrine solution of the NLSE, it is significantly more involved and contains polynomials of fourth order rather than second order in the corresponding expressions. The correct limiting case of Peregrine solution appears when the extension parameter of the SSE is reduced to zero.

Appeared in

  • Phys. Lett. A, 376 (2012) pp. 1558--1561.

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