Bandelow, U.Ankiewicz, AdrianAmiranashvili, S.Akhmediev, Nail2020-05-142020-05-141054-1500http://hdl.handle.net/1885/204307We 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.The authors gratefully acknowledge the support of the Australian Research Council (Discovery Projects DP140100265 and DP150102057) and support from the Volkswagen Stiftung. N.A. is a recipient of the Alexander von Humboldt Award. U.B. acknowledges support by the German Research Foundation in the framework of the Collaborative Research Center 787 “Semiconductor Nanophotonics” under project B5. Sh.A. acknowledges support of the German Research Foundation under Project No. 389251150.application/pdfen-AU© 2018 AIP Publishing2018-05-1710.1063/1.50306042022-12-11