WIAS Preprint No. 2510, (2018)

Generalized Sasa--Satsuma equation: Densities approach to new infinite hierarchy of integrable evolution equations


Authors

  • Ankiewicz, Adrian
  • Bandelow, Uwe
    ORCID: 0000-0003-3677-2347
  • 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, integrable equations, solitons

DOI

10.20347/WIAS.PREPRINT.2510

Abstract

We derive the new infinite Sasa-Satsuma hierarchy of evolution equations using an invariant densities approach. Being significantly simpler than the Lax-pair technique, this approach does not involve ponderous 3 x 3 matrices. Moreover, it allows us to explicitly obtain operators of many orders involved in the time evolution of the Sasa-Satsuma hierarchy functionals. All these operators are parts of a generalized Sasa-Satsuma equation of infinitely high order. They enter this equation with independent arbitrary real coefficients that govern the evolution pattern of this multi-parameter dynamical system.

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