Nonlinear waves propagation for a generalized KdV-type evolution equation: solitons, breathers and their interactions
Keywords:
GERFM, Wave transformation, Rational trial function, Solitary waves, Dynamical AnalysisAbstract
In this research, we analytically investigate the solutions of a generalized nonlinear higher-order Korteweg–de Vries (KdV)-type partial differential equation, which contains the Sawada-Kotera equation as its particular form. In the process of finding the analytical solutions, generalized exponential rational function (GERF) method is employed as the solution technique, in which the investigated nonlinear PDE is transformed into a simplified ordinary differential equation (ODE) utilizing a traveling wave transformation. A rational trial function involving exponential function terms is then considered for the reduced simple equation to derive the analytical solutions. We consider several families of parameters to analyse distinct solutions for the families of the trial function. The obtained solutions suggest the presence of a rich variety of nonlinear wave structures, such as bright and dark solitons, breathers, and oscillatory periodic background waves. The dynamical behavior of the solutions is analysed graphically using the symbolic system \textit{Mathematica,} with appropriate choices of parameters. The wave propagation and its physical behaviour are illustrated in 2D and 3D graphics. The investigated equation has physical applications in applied mathematics, plasma physics, fluid dynamics, soliton theory, and other nonlinear sciences.References
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