| dc.description.abstract |
The nonlinear evolution equations (NLEEs), which have gained prominence recently, explain many real-world phenomena. In this research, we have investigated two NLEEs to establish the widespread and consistent abundant close-form stable wave solutions by implementing the new auxiliary equation method and the unified method. In this thesis, the (3+1)-dimensional modified Korteweg de-Varies-Zakharov-Kuznetsov equation (mKdV-ZKE) is examined by the new auxiliary equation method and the unified method. Also, the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation (BLMPE) is analyzed through the new auxiliary equation method and the unified method. Using computational software such as MATLAB and MAPLE, the solutions illustrate several structures of solitons and varies their nature and loci demonstrated in three-dimensional (3D), contour, and combined two-dimensional (2D) graphs for the distinct values of Kerr nonlinearity, nonlinear coefficient, wave number, wave speed, etc. However, by comparing our results to previously published literature using different approaches and analyzing the solutions by drawing figures for various values of the associated parameters, we find that the features of the solutions are important in parameter selection. Furthermore, we also show the connection between the values of the various kinds of parameters and the physical reasoning behind the found solution. We demonstrated that the major reason why wave profiles behave differently when their related free parameters change. Examined are the effects of wave velocity and different unrestricted parameters on the wave profile. However, sketching the solutions for different values of the associated parameters and examining the results of these techniques demonstrate that the parametric values significantly affect the characteristics of the solutions. With a few limitations, these techniques are reliable, straightforward, efficient, and simple to use. |
en_US |