On the solitary wave solution of the viscosity capillarity van der Waals p-system along with Painleve analysis

Abstract

This work proposes two well known schemes, painleve analysis test and auxiliary equation mapping (AEM) algorithm to find new solitary wave solutions for van der Waals p-system (VDW) in the viscosity capillarity version. For the clarity of physical features, new solitary wave solutions like periodic, kink and anti kink type, doubly periodic, trigonometric, singular, rational, combined soliton like solutions and hyperbolic solutions, etc. are articulated coupled with graphically patterns 2D, 3D and density plots to visualize the dynamics of our model. This study reveals that the methods used are simple, reliable, unambiguous and concise as compared to many other techniques for solving nonlinear partial differential equations (NLPDE). A new direct way to solve NLPDEs is provided using this approach. The method allows one to obtain new accurate solutions of the solitary wave that cannot be obtained using other methodologies, and it can be implemented on a computer using computer algebraic systems such as Mathematica or Maple.