Generalized Sasa--Satsuma equation: Densities approach to new infinite hierarchy of integrable evolution equations
- Ankiewicz, Adrian
- Bandelow, Uwe
- Akhmediev, Nail
2010 Mathematics Subject Classification
- 37K10 37K40 35Q55
2008 Physics and Astronomy Classification Scheme
- 02.30.Ik 05.45.Yv 42.65.Tg 47.35.Fg
- Sasa--Satsuma equation, integrable equations, solitons
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.
- Z. Naturforsch., 73 (2018), pp. 1121--1128, DOI 10.1515/zna-2018-0377 .