Solution of KDV and MKDV equation by using (g’/g)- expansion method and space-time fractional methods
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Date
2023
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UMT, Lahore
Abstract
The complex nature of nonlinear evolution equation has always remained a hot debate in the field of plasma physics. Due to its complexity, it is quite challenging to find exact solutions to it using traditional techniques. Therefore, a methodology has been devised which we call g g ' expansion method. In this investigation we work on space-time KdV, mKdV, KdV-MKdV and space-time fractional ‘KdV-MKdV’ equation. With the help of g g ' expansion method and extended g g ' expansion method. Several types of new mathematical exact solutions are obtained, along-with solutions for hyperbolic relations, trigonometric variable functions, and rational expressions. By applying the said technique, we found that these are novel techniques in finding exact mathematical solutions of nonlinear partial differential equations (PDEs) and nonlinear fractional PDEs. Furthermore, graphical representations in the form of two-dimensional and three-dimensional are also presented to highlight the results of our new findings by using MATHEMATICA programming.