Dynamics of nonlinear diverse wave propagation to Improved Boussinesq model in weakly dispersive medium of shallow waters or ion acoustic waves using efficient technique

In this study, we will extract new impressive visions for the exact traveling wave solutions to the Improved Boussinesq dynamical model of water wave problems in a weakly dispersive medium of shallow water or ion acoustic waves under the damping constant of internal friction. In this study, the new extended direct algebraic method has been used to generate some new and more universal exact traveling wave solutions. The recovered solutions are divided into single (kink, anti-kink, singular), bright, dark, complex, and combo forms. During the derivation, new families of hyperbolic, exponential, and periodic wave solutions with arbitrary parameters also emerged. The achieved outcomes are examined using three-dimensional plotline, contour plot, and two-dimensional plotline for definite parametric values. Additionally, the results have been compared with other existing results in the literature to show their uniqueness. Moreover, the findings show that the method taken is successful, simple, and can be use even to complicated phenomena, and this work will also be helpful to a large number of engineering model specialists and in many other areas of physics.