Three different integration schemes for finding soliton solutions in the (1+1)-dimensional Van der Waals gas system

Abstract

This paper explores three distinct integration schemes applied to the problem of finding soliton solutions in the (1+1)-dimensional Van der Waals gas system. The methods employed include the Enhanced Kudryashov’s method, the Sine–Gordon equation method, and the Projective Riccati equations method. Each of these techniques offers a unique approach to solving the system’s equations and finding soliton solutions. By examining and comparing the results obtained from these different integration schemes, this study aims to provide valuable insights into the behavior and properties of solitons in the Van der Waals gas system.