The Camassa-Holm nonlinear Schr\"{o}dinger equation is a deformation of the nonlinear Schr\"{o}dinger equation which was developed in the context of transforming the hierarchical structure of integrable systems. Also the Boussinesq equation is a mathematical model that is capable of simulating weakly nonlinear and long-wave approximations. This model finds its applications in various fields such as coastal engineering, and numerical models for water wave simulation in harbors and shallow seas. The two considered equations have significant applications in mathematical physics and their exact wave solutions are essential to understand their dynamical behavior. The governing equations are solved analytically by applying extended~$\left( \nicefrac{G'}{G^2} \right)$-expansion approach. Dark solitons, bright solitons, and periodic waves are observed from the obtained results. Graphs are presented to depict the behavior of some of the retrieved dynamical wave structures.
