This paper examines the soliton phase shift using a simplified third-order generalized nonlinear Schrodinger equation (3-order GNLSE). In this investigation, we employ a new direct algebraic (NDA) technique to solve these models. All evaluated solutions are put to the test using two modern numerical (trigonometric quantic and cubic B-spline) schemes. The necessary criteria for implementing numerical systems are derived from the computational solutions. As the model captures the dynamical behavior of ultra-short pulses in optical fiber and quantum fields, this research is crucial. As a wave model, the 3-order GNLSE equation may be used to illustrate the wave nature of matter. It is regarded as a quantum-mechanical state function since it may represent the dynamical and physical behavior of atoms and transistors. The exactness of the answers is shown through two-dimensional, three-dimensional, and contour charts (matching between analytical and numerical solutions). The answers presented in the research are innovative in comparison to earlier findings.
AMS classification: 35C08; 37K40; 35C07; 37K40.