Lump and interaction solutions to the (3+1)-dimensional Burgers equation*

Abstract

The (3+1)-dimensional Burgers equation, which describes nonlinear waves in turbulence and the interface dynamics, is considered. Two types of semi-rational solutions, namely, the lump–kink solution and the lump–two kinks solution, are constructed from the quadratic function ansatz. Some interesting features of interactions between lumps and other solitons are revealed analytically and shown graphically, such as fusion and fission processes.