Construction of rogue waves and conservation laws of the complex coupled Kadomtsev–Petviashvili equation

Abstract

In this work, the solutions of the real coupled Kadomtsev–Petviashvili equations (KPEs) are obtained and they are used to find the ones of the complex system. To this end, the extension theorem is used. The formation of rogue wave (RW) is shown to occur via inelastic collisions of lines-lump solitons and periodic waves and also of two elliptic waves. The quadratic invariant is used to show the phase portrait and bifurcation through the contour plot. Further, the conservation laws (CLs) are constructed by means of new conservation theorem by finding the governing system of equation. The results are given, work consolidated from a previous work, by the first two authors, for suggesting a mechanism for the formation of RW when the complex Korteweg–de Vries equation was studied. Based on the exact solutions found here, numerical computations are carried out and they are represented graphically. Finally, the unified method (UM) can be applied to solve a variety of partial differential equations in science and engineering.