Abundant exact solutions of a (3+1)-dimensional burgers like equation on the periodic background

The purpose of this paper is to focus on improving the unified F-expansion method and investigating the evolution phenomenon of solitary waves on periodic wave background. Based on the unified F-expansion method, the main innovation of this paper is to propose multiple unified F-expansion method and successfully construct a series of complexiton solutions for a (3+1) dimensional Burgers like equation, further enriching the types and quantities of exact solutions. In addition, compared with the multiple G'/G expansion method, the complexiton solutions composed of multiple Jacobian elliptic functions presented in this paper have new structural characteristics, which can explain two novel nonlinear phenomena: one type of complexiton solutions can describe the propagation process of solitary waves on periodic wave background; Another type of complexiton solution can exhibit the propagation process of solitary waves on composite periodic wave background. These novel findings and conclusions in this paper have greater value and significance than the propagation of solitary waves on zero background. Furthermore, the multiple unified F-expansion method can also solve variable coefficient nonlinear evolution equations, high-order nonlinear evolution equations, and coupled nonlinear complex systems. Therefore, the multiple unified F-expansion method provides an effective approach for the study of nonlinear theory.