A Study for Analytical Solutions to Nonlinear Evolution Equations with Analytical Approach
Keywords:
Kink-type solitons, Breathers, Solitons, GERFM, Analytical solutionsAbstract
This research presents an analytical study of the (3+1)-dimensional KdV-type nonlinear evolution equation using the Generalized Exponential Rational Function Method (GERFM). This approach is an effective analytical technique for obtaining analytical solutions of nonlinear partial differential equations arising in plasma physics, fluid dynamics, nonlinear optics, and wave propagation phenomena. The governing nonlinear equation is transformed into an ordinary differential equation through a travelling wave transformation. And, a homogeneous balance principle is applied to construct suitable exponential rational trial functions. By employing the GERFM approach, several exact analytical solutions are obtained and classified into different families representing soliton waves, kink-type waves, periodic structures, and singular wave solutions. It further analyzes the solutions graphically with two- and three-dimensional plots. This graphical analysis is carried out with Mathematica to study the wave propagation behavior, stability, localization, and interaction of nonlinear waves under appropriate parameters. The study confirms the efficiency and applicability of GERFM in investigating higher-dimensional nonlinear evolution equations and provides useful insights into multidimensional wave dynamics.
References
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Data Availability Statement
Data sharing is not applicable to this article as no new data were created or analyzed in this study.
