Analytical solution of non-linear partial differential equation by using the extended (𝐆�′/𝐆�) expansion method with non-linear auxiliary equation

Abstract

Among some new methods, these were introduced to find the exact solution of Non-Linear Partial Differential Equations (NLPDEs), (G'/G) expansion method proposed by Mingliang Wang, is straightforward and easy to handle as it gives rich new solutions. On the other hand, Solitons play a dynamic role in the field of engineering applications and, nonlinear science and it delivers more perception into the related nonlinear scientific occurrences by leading to forthcoming scientific research. So, to check the validity and effectiveness of our method we have implemented the extended (G'/G) expansion method to the (2+1) dimensional breaking soliton equation. The outcomes we have found here, are more common, successfully recovered the most of the earlier recognized results which have been established by other sophisticated methods. We have found some new results as well which will lead us to study some new phenomena in future. We have stated the travelling wave solutions here by three types of family. They are the hyperbolic family, the trigonometric family and, the rational family. The results along with the graphical illustration have revealed the high productivity of this algorithm with trustworthiness.