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The paper discusses investigating the behavior of the discrete nonlinear Schrödinger (DNLS) system. This technique combines the exponential function method and the rational function method to obtain exact solutions for a wide range of nonlinear differential-difference equations (NDDEs). The objective is to utilize the generalized exponential rational function (GERF) technique to analyze and understand the dynamics of the DNLS system. Overall, this research contributes to advancing our knowledge of nonlinear dynamics in optical fibers and establishes a solid foundation for further exploration of soliton applications. • We focused on investigating discrete soliton solutions in a system that describes the propagation. • The investigation of these soliton solutions opens up new avenues for applications in optical communications. • We discovered various families of soliton solutions. [ABSTRACT FROM AUTHOR]