Accurate Coiflet wavelet solution of extended [formula omitted]-dimensional Kadomtsev–Petviashvili equation using the novel wavelet-homotopy analysis approach

Abstract

We established a novel wavelet-homotopy analysis technique to give accurate solutions to nonlinear wave problems with unsteady state, which is the originality of the paper. The extended (2+1)-dimensional Kadomtsev–Petviashvili equation is taken as the research object owing to its complexity and importance. The convergence of the proposed technique is proved. The modulation instability is employed to determine the range of the normalized wave numbers of the transformed traveling wave equation. The validity and reliability of our results are checked via a rigid comparison with analytical solutions. Results and the comparison with the numerical solutions reveal that the proposed technique maintains capabilities of the homotopy analysis method for strong nonlinear processing and the wavelet technique for excellent local detail representation. It is expected that the proposed method can be used as an alternative tool to analyze more complex wave problems such as rogue wave or shock wave problems.