Analytical methods: Nonlinear longitudinal wave equation in a magnetoelectro-elastic circular rod, foam drainage and modified Degasperis–Procesi models arising in nonlinear water wave models

We form the analytical solitary wave solutions with the execution of generalized direct algebraic technique on three well-known nonlinear wave models, namely, called foam drainage, longitudinal magnetoelectro-elastic circular rod and modified Degasperis–Procesi equations. The derived solutions are hyperbolic functions in which some are plotted graphically on meticulous values to the parameters which provides the basic knowledge to understand physical significant of these three wave models. The obtained solutions show the efficiency and precision of our scheme. These derived new results prove that our novel technique is awfully effective and can be productive as a instrument solving for sundry other nonlinear evolution equations.