New shock-wave and periodic-wave solutions for some physical and engineering models: Vakhnenko-Parkes, GEWB, GRLW and some integrable equations

In this work, the modified unified expansion and the Bernoulli sub-equation methods are implemented to extract new shock-wave and periodic-wave solutions for important physical and engineering models. We study four models; the Vakhnenko-Parkes (VP) equation, the generalized equal width-Burgers (GEWB) equation with $p \in \{1, 2\}$ and the generalized regularized-long-wave (GRLW) equation by the modified unified method, whereas the first-second fourth-order integrable equations by the Bernoulli sub-equation method. Shock-wave and periodic wave solutions are obtained for these models. All obtained solutions are verified and categorized regarding its physical structures.