Integrability and gauge equivalence of the reverse space–time nonlocal Sasa–Satsuma equation

The integrability of the reverse space–time nonlocal Sasa–Satsuma equation in the Liouville sense is established by showing the existence of infinitely many conservation laws and putting into a bi-Hamiltonian form. Further, we show that the nonlocal Sasa–Satsuma equation for focusing case and defocusing case is, respectively, gauge equivalent to a generalized Heisenberg-like equation and a modified generalized Heisenberg-like equation. Finally, by using of special variable transformations, various kinds of nonlinear waves are obtained from those of the classical counterpart.