Optical Solutions of the Nonlinear Kodama Equation with the M-Truncated Derivative via the Extended (<i>G</i>^′/<i>G</i>)-Expansion Method

Abstract

The main purpose of this article is to study the optical solutions of the nonlinear Kodama equation with the M-truncated derivative by using the extended (G′/G)-expansion method. Firstly, the nonlinear Kodama equation with the M-truncated derivative is transformed into a nonlinear ordinary differential equation based on the principle of homogeneous equilibrium and the traveling wave transformation. Secondly, the optical solutions of the nonlinear Kodama equation with the M-truncated derivative are constructed by using the extended (G′/G)-expansion method. Finally, three-dimensional, two-dimensional, and contour maps of partial solutions are obtained by using Matlab R2023b mathematical software.

Keywords

• nonlinear Kodama equation
• optical solution
• traveling wave transformation
• M-truncated derivative