Kadomtsev–Petviashvili equation in relativistic fluid dynamics

The Kadomtsev–Petviashvili (KP) nonlinear wave equation is the three dimensional generalization of the Korteveg-de Vries (KdV) equation. We show how to obtain the cylindrical KP (cKP) and cartesian KP in relativistic fluid dynamics. The obtained KP equations describe the evolution of perturbations in the baryon density in a strongly interacting quark gluon plasma (sQGP) at zero temperature. We also show the analytical solitary wave solution of the KP equations in both cases.

► We derive the Kadomtsev–Petviashvili equation in relativistic hydrodynamics.
► The Kadomtsev–Petviashvili is for baryon perturbations in quark gluon plasma.
► We solve analytically the Kadomtsev–Petviashvili equation.
► We study soliton conditions for the Kadomtsev–Petviashvili equation.
► We plot solitonic solutions of the Kadomtsev–Petviashvili equation.