New solitary wave and other exact solutions of the van der Waals normal form for granular materials

Abstract

The investigation of exact solitary wave solutions to the nonlinear partial differential equation plays an important role to understand any physical phenomena in diverse applied fields. The current work is related to the most prominent nonlinear model named as the van der Waals normal form that appeared naturally and also industrially for the granular materials. In oceanography, the sea ice, sand and snow are some examples of aforesaid matter among others. We employ two novel integration approaches named as the simplest equation method and the expa function method to explore the above mentioned van der Waals model. As a backlash, many new solitary waves and other exact solutions are retrieved. The obtained results depict that the used approaches are simple and effective to deal with nonlinear models. Also, the numerical simulation of some solutions via two and three dimension graphical configurations are presented for certainty and exactness.

Keywords

• Van der Waals equation
• Novel integration schemes
• Solitary wave solutions