Extended and high-order complex-valued evolution equations are found ideally to model complex nonlinear scenarios, having perfectly featured the underlined physical assumptions. Thus, with the identified applications of the classical Chen-Lee-Liu equation, in particular, in different realms of nonlinear sciences, this study proposes several extensions to the Chen-Lee-Liu equation and its perturbed form by incorporating the cubic-quintic nonlinearity law and a resonant term with the view to extending the applicability spectrum of the classical model. Method-wise, the modified extended tanh method, in favor of its mathematical flexibility and effectiveness in handing both the real- and complex-valued evolution equations, is utilized as the primary tool for deriving exact solutions for the new models, in addition to being complemented by the modified Kudryashov method to extract additional solitonic expressions. The study also performs a linearization of the generalized model to conduct dispersion relation and modulation instability analyses. Several periodic and solitonic solutions are obtained analytically, and the characteristic equation governing the overall wave dynamics is derived. A numerical investigation of the involved parameters reveals that the inclusion of the resonant term enhances wave dispersion in the medium, while the added perturbation terms act to suppress the dispersion of harmonic waves in the complex system. This way, one notes that these new models provide an avenue to controlling transmission of field in the governing media, including fluid medium, optical fibers, or even in optical communication processes where pulsification trend is of paramount importance. Overall, the findings of this research are expected to have significant implications in fluid dynamics, nonlinear optics, quantum physics, and optoelectronics, among other fields in nonlinear science.

This study examines a class of Boussinesq equations with sixth-order using two promising analytical methods. The equation in question is among the frontier evolution equations with significant relevance in nonlinear lattice dynamics. To study this model, the Kudryashov method and the modified auxiliary equation method are employed due to their analytical precision in constructing several exact wave solutions for the model under examination. As expected, the methods yield many valid solution sets that satisfy all the underlying assumptions of the model. Finally, some of the obtained wave solutions are graphically illustrated, taking into account the parameter values of the model.