A Homotopy-Based Technique to Compute Soliton Solutions of Kadomtsev-Petviashvili Equation

Purpose Kadomtsev-Petviashvili (KP) equation, a (2+1) dimensional equation, is used to model various physical systems, such as the weakly dispersive waves, two-dimensional shallow-water waves, ion-acoustic waves in plasmas, Bose-Einstein condensation, etc. The KP equation is a classical model for testing and establishing new mathematical methods. A newly proposed homotopy-based perturbation method (LH) (which worked very well in several physical systems) is employed to solve the KP equation to test its effectiveness. Methods In LH, an expansion of frequency and a parameter (h) (to control convergence) are incorporated in the framework of the homotopy perturbation method (HPM) to improve the accuracy of solutions by retaining its simplicity. Results and conclusions LH results are compared with those obtained from some of the available approximation methods for different parameter set values. LH method produces simple and compact analytical expressions for approximate solutions with high accuracy, which is better than HAM and HPM, especially with the higher order of approximations.