Lump-Type Solutions, Mixed Solutions and Rogue Waves for a (3+1)-Dimensional Variable-Coefficients Burgers Equation

Abstract

In this work, we consider the (3+1)-dimensional Burgers equation with variable coefficients, which is frequently used to define the motion of solitary waves. Abundant lump waves are constructed by taking the ansatz as a rational function. Furthermore, mixed solutions utilizing lump waves, rogue waves, and kink solitons are obtained by combining the rational function with an exponential function, resulting in fission and fusion phenomena.

Keywords

• variable-coefficients Burgers equation
• lump solutions
• lump soliton solutions
• rogue waves