  In this paper, we investigate the nonlocal generalized Sasa-Satsuma (ngSS)
equation based on an improved Riemann-Hilbert method (RHM). Different from the
traditional RHM, the $t$-part of the Lax pair plays a more important role
rather than the $x$-part in analyzing the spectral problems. So we start from
the $t$-part of the spectral problems. In the process of dealing with the
symmetry reductions, we are surprised to find that the computation is much less
than the traditional RHM. We can more easily derive the compact expression of
$N$-soliton solution of the ngSS equation under the reflectionless condition.
In addition, the general high-order $N$-soliton solution of the ngSS equation
is also deduced by means of the perturbed terms and limiting techniques. We not
only demonstrate different cases for the dynamics of these solutions in detail
in theory, but also exhibit the remarkable features of solitons and breathers
graphically by demonstrating their 3D, projection profiles and wave
propagations. Our results should be significant to understand the nonlocal
nonlinear phenomena and provide a foundation for fostering more innovative
research that advances the theory.
