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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 × 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 generalised Sasa–Satsuma equation of infinitely high order. They enter this equation with independent arbitrary real coefficients that govern the evolution pattern of this multiparameter dynamical system.

Generalised Sasa–Satsuma Equation: Densities Approach to New Infinite Hierarchy of Integrable Evolution Equations