New Function Solutions of Ablowitz-Kaup-Newell-Segur Water Wave Equation via Power Index Method

In this article, the applications of the Power Index Method (PIM) are presented to ascertain function solutions of the AKNS equation. We find out adequate explicit general solutions for the AKNS in the form of exponential, trigonometric, and logarithmic functions which have their importance in the physical sciences. We have used function transformations in which indexes of independent variables are nonrestricted parameters. During our investigation, we have seen that the nonlinear AKNS can be reduced to linear ODE by using PIM. All the solutions contain independent variables with parameters, and they are graphically represented by choosing suitable values of parameters.