Our research focused on the analytical treatment of the (mK-dV) model, and as a result, we discovered some new and more general families of exact solutions with potential applications in reading the qualitative analysis of many nonlinear wave phenomena in a more precise manner. Furthermore, these findings have a significant impact on the development of theories of soliton dynamics, adiabatic parameter dynamics, and quantum mechanics. We also used the auxiliary equation mapping approach to analyse the two-dimensional modified Korteweg-de Vries (mK-dV) equation, which arises in plasma physics and regulates ion-acoustic solitary waves for their asymptotic behaviour due to electron entrapment. Using this approach, we were able to produce a wide range of accurate travelling wave solutions, including semi half bright, bright, dark, semi half dark, doubly periodic, combined, periodic, half hark, and half bright through three parametric values, which is our technique's key point of distinction. These findings have a wide range of applications in quantum mechanics, biomedical problems, soliton dynamics, plasma physics, nuclear physics, optical physics, fluid dynamics, electromagnetism, industrial studies, mathematical physics, biomedical problems, and a variety of other natural and physical sciences. For a more precise physical dynamical depiction of our conclusions, we used Mathematica to create graphs in various dimensions to better comprehend the many new dynamical forms of solutions.
Nadia Cheemaa,
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China.
Aly R. Seadawy,
Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia and Department of Mathematics, Faculty of Science, Beni-Suef University, Egypt.
Hafiza Tasneem Nazish,
Department of Mathematics and Statistics, University of Agriculture Faisalabad 38040, Pakistan.
Please see the link here: https://stm.bookpi.org/NTPSR-V4/article/view/6933
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