Painlevé property and approximate solutions using Adomian decomposition for a nonlinear KdV-like wave equation

In this paper, we have discussed the integrability of a nonlinear partial differential equation, with a focus on the Painlevé property, the compatibility condition and the Bäcklund transformation. Afterwards, the Adomian decomposition method, which accurately computes the series solution, has been used to obtain an approximate solution. The convergence analysis based on the wave number and nonlinearity parameter has also been performed using graphical interface of a numerical solver.