New variable separation solutions, localized structures and fractals in the (3+1)-dimensional nonlinear Burgers system

Abstract

Applying the extended Riccati mapping approach to the (3+1)-dimensional nonlinear Burgers system, we obtain new variable separation solutions which contain an arbitrary function. With the help of numerical simulation of Mathematica, abundant special types of new localized excitations and fractals are discussed by selecting the arbitrary function appropriately. The solutions indicate that the extended Riccati mapping approach is valid for solving a class of (3+1)-dimensional nonlinear equations and can obtain much more abundant localized excitations than that of the (2+1)-dimensional nonlinear equations.