A symbolic computation approach and its application to the Kadomtsev-Petviashvili equation in two (3+1)-dimensional extensions

This work examines the multi-rogue-wave solutions for the Kadomtsev-Petviashvili (KP) equation in form of two (3+1)-dimensional extensions, which are soliton equations, using a symbolic computation approach. This approach is stated in terms of the special polynomials developed through a Hirota bilinear equation. The first, second, and third-order rogue wave solutions are derived for these equations. The interaction of many rogue waves is illustrated by the multi-rogue waves. The physical explanations and properties of the obtained results are plotted for specific values of the parameters alpha and beta to understand the physics behind the huge (rogue) wave appearance. The figures are represented in three-dimensional, and the contour plots and the density are shown at different values of parameters. The obtained results are significant for showing the dynamic actions of higher-rogue waves in the deep ocean and nonlinear optical fibers.

Automated summary

This work investigates the multi-rogue-wave solutions for the Kadomtsev-Petviashvili (KP) equation in two (3+1)-dimensional extensions. The symbolic computation approach and special polynomials developed from the Hirota bilinear equation are utilized. The first, second, and third-order rogue wave solutions for these equations are derived. The physical properties and interactions of multiple rogue waves are analyzed and visualized. The obtained results are significant for understanding the dynamics of higher-order rogue waves in the deep ocean and nonlinear optical fibers.