Obtaining soliton solutions of the perturbed Radhakrishnan-Kundu-Lakshmanan model with M-truncated derivative

This study explores the soliton solutions for the perturbed Radhakrishnan-Kundu-Lakshmanan (RKL) equation which includes M-truncated derivative. Initially, a wave transformation technique is employed for the RKL equation, yielding a nonlinear ordinary differential equation (NODE). Then, the NODE is solved using the new Kudryashov method. A candidate solution and its related derivatives are incorporated into the NODE, resulting in a polynomial expression. A system of algebraic equations emerges by equating coefficients of terms with similar degrees to zero. Solving this system provides the identification of unknown variables in the candidate solution, thereby yielding the solutions to the RKL equation. Diverse illustrations of the obtained solutions are presented via contour, two-dimensional, and three-dimensional plots. The findings of this research may present potential implications for future studies in nonlinear optics.