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In this paper, we investigate the nonlocal generalized Sasa-Satsuma (ngSS)equation based on an improved Riemann-Hilbert method (RHM). Different from thetraditional RHM, the $t$-part of the Lax pair plays a more important rolerather than the $x$-part in analyzing the spectral problems. So we start fromthe $t$-part of the spectral problems. In the process of dealing with thesymmetry reductions, we are surprised to find that the computation is much lessthan 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 equationis also deduced by means of the perturbed terms and limiting techniques. We notonly demonstrate different cases for the dynamics of these solutions in detailin theory, but also exhibit the remarkable features of solitons and breathersgraphically by demonstrating their 3D, projection profiles and wavepropagations. Our results should be significant to understand the nonlocalnonlinear phenomena and provide a foundation for fostering more innovativeresearch that advances the theory.

Simple and high-order $N$-solitons of the nonlocal generalized Sasa-Satsuma equation via an improved Riemann-Hilbert method