Application of the Functional Variable Method to Some Nonlinear Evolution Equations (Journal of Nonlinear Modeling and Analysis, 2025)
The functional variable method is a highly effective approach for deriving exact solutions to nonlinear evolution equations. It offers broad applicability in addressing nonlinear wave equations. In this paper, the functional variable method is employed to obtain soliton solutions for the Radhakrishnan-Kundu-Lakshmanan (RKL) equation and the Landau-Ginzburg-Higgs equation. Exact solutions play a crucial role in uncovering the internal mechanisms of physical phenomena. Graphical representations of the obtained optical soliton solutions are provided to illustrate some of their physical parameters.