Different wave patterns for (2 + 1) dimensional Maccari’s equation

In this paper, we are concerned with the (2 + 1) dimensional Maccari’s equation. With the aid of Truncated Painlevé Approach (TPA), the localized solutions have obtained in terms of arbitrary functions. By using the suitable arbitrary functions present in the solution, we have generated the multi-rogue waves, rogue wave doublet and lump solutions. Moreover, through selecting the values of control parameters, dynamical behaviors for the obtained multi-rogue wave, rogue wave doublet and lump solutions are graphically illustrated with the aid of Mathematica tool. The results obtained through this investigation will be beneficial for understanding the dynamics of nonlinear waves in higher dimensional Maccari systems.