Abstract
This work examines an n-component reverse-space-time nonlocal generalized Sasa-Satsuma system within the Riemann-Hilbert framework. The equation under consideration is obtained from an unreduced 2n-component coupled generalized Sasa-Satsuma system after the constraint rj(x,t)=−uj(−x,−t) is imposed. Owing to this nonlocal reduction, the dependent variables at (x, t) are linked with those at (−x,−t), which in turn modifies the symmetry structure of the corresponding spectral problem. We derive the Lax representation for the reduced model and analyze the associated Jost eigenfunctions, scattering data, and analyticity properties in the complex λ-plane. These spectral results are then used to formulate a matrix Riemann-Hilbert problem. In the reflectionless setting, the resulting meromorphic Riemann-Hilbert problem leads to a general N-soliton formula. For the special case n=2, the constraints imposed by the nonlocal reduction on the discrete eigenvalues and eigenvectors are determined explicitly, and single- and double-soliton solutions are constructed for admissible parameter choices.