Abstract
The present study reveals cubic–quartic optical solitons with the perturbed Biswas–Milovic equation having Kudryashov’s nonlinear form and two generalized non-local laws for the first time. The Hamiltonian perturbation terms are presented via the maximum intensity parameter. Singular, bright-singular and dark solitons are retrieved using two mathematical schemes that are the modified Kudryashov’s procedure and the extended auxiliary equation algorithm. These solitons are extracted via certain restrictions.