(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Bandelow, Uwe; Ankiewicz, Adrian; Amiranashvili, Shalva; Pickartz, Sabrina; Akhmediev, Nail
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 sixthorder 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.
