An efficient analysis for N-soliton, Lump and lump–kink solutions of time-fractional (2+1)-Kadomtsev–Petviashvili equation

Abstract

Solutions of the nonlinear physical problems are significant and a vital topic in real life while the soliton based algorithms are promising techniques to analyze the solutions of various nonlinear real-world problems. Herein, we are reporting some new soliton solutions including N-soliton, lump and lump–kink for (2+1)-Kadomtsev–Petviashvili of fractional-order α arising in mathematical physics. Multiple exp-function approach and bilinear form has been used to investigate the N-soliton and lump, lump–kink solutions of the discussed fractional-order problem. These methods convert the nonlinear partial differential equations into nonlinear algebraic equation having exponential functions. Furthermore, the method is oriented to the comfort of use and fitness of computer algebra systems and provides a direct and systematical solution procedure which generalizes Hirota’s perturbation scheme. Graphical representations (2D and 3D) of few specific presented multiple, lump and lump–kink solutions has been made to show the characteristics of multiple, lumps and lump–kinks as well as significant effects of α are plotted for each solution. Moreover, the amplitude of the waves is examined for various values of space variables in x and y direction as well as particular values of α as time varies. It is noticed that as α→1the solution turn into three wave and lump–kink solutions which is asserted via set of graphs. The higher values of space variable y are causing a decrease in the amplitude of the wave whereas the higher values of α are providing a higher amplitude of the wave. Hence, the attained results for nonlinear time fractional (2+1)-Kadomtsev–Petviashvili equation are endorsing the efficiency and appropriateness of multiple exp-function to analyze the N-soliton solutions. It is important to highlight that said method could be extended to diversify problem of physical nature.