Abstract In this manuscript, we investigate the analytical and soliton solutions of the cubic-quintic-
septic law for the perturbed Biswas-Milovic equation, considering spatio-temporal and chro-
matic dispersions. The perturbed Biswas-Milovic equation with the spatio-temporal and
chromatic dispersion terms provides a comprehensive study for describing nonlinear opti-
cal wave propagation in optical fiber. We use the wave transformation to reduce the main
equation to a nonlinear ordinary differential equation. Through the transformation of the
original equation into a more simplified form, it aims to attain a more profound comprehen-
sion of the fundamental dynamics of the system. We retrieve the analytical solutions of the
presented model by implementing the new Kudryashov technique and a subversion of the
new extended auxiliary equation approach. Besides, bright, singular, and V-shape soliton
structures are represented. Moreover, we analyze the soliton behavior influenced by various
parameters. The analysis of the parameter influences reveals the complicated relationship
governing the dynamics of the perturbed Biswas-Milovic model.