WIAS Preprint No. 2487, (2018)

Sasa--Satsuma hierarchy of integrable evolution equations


Authors

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

2010 Mathematics Subject Classification

  • 37K10 37K40 35Q55

2010 Physics and Astronomy Classification Scheme

  • 02.30.Ik 05.45.Yv 42.65.Tg 47.35.Fg

Keywords

  • Sasa--Satsuma equation, Lax pair, integrable hierarchy

DOI

10.20347/WIAS.PREPRINT.2487

Abstract

We present the infinite hierarchy of Sasa-Satsuma evolution equations. The corresponding Lax pairs are given, thus proving its integrability. The lowest order member of this hierarchy is the nonlinear Schrödinger equation, while the next one is the Sasa-Satsuma equation that includes third-order terms. Up to sixth- order terms of the hierarchy are given in explicit form, while the provided recurrence relation allows one to explicitly write all higher-order terms. The whole hierarchy can be combined into a single general equation. Each term in this equation contains a real independent coefficient that provides the possibility of adapting the equation to practical needs. A few examples of exact solutions of this general equation with an infinite number of terms are also given explicitly.

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