The Perturbed Potential Kadomtsev-Petviashvili Equation: Bilinear Form, Multi Shock, Kinky-Breather, Resonant Y-Type Shock Solutions

This article claimes the integrability of the perturbed potential Kadomtsev-Petviashvili (pPKP) equation in (3+1)-dimensions through the bilinear Bäcklund transformation. Using the bilinear form of the aforementioned problem, new kinds of shock solutions are produced via careful selection of the auxiliary functions. On the basis of vector options in the solution space, the kinky breather solution is explored from a two-shock solution. The three-shock seed solution is used to offer an explanation of the interplay between the one-order kinky breather solution and the one-shock solution. The wave interaction of the shock with breathers and another shock is studied from the numerical understanding. Under certain compatibility conditions, the K-shock solutions are transformed into the resonant Y-type shock wave solution. Specific values of the related parameters in the current system are used to show the resulting solutions in various patterns.