Volume 36 • Number 3 • 2013   • A Generalization of the $G'/G$-Expansion Method and Its Application to Jimbo--Miwa Equation Sheng Zhang Abstract. A generalization of the $G'/G$-expansion method combined with Liu's theorem is proposed to construct exact solutions of the (3+1)-dimensional Jimbo--Miwa equation. As a result, more general travelling wave solutions with parameters are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. Some of the obtained hyperbolic function solutions and trigonometric function solutions contain an explicit external linear function of $\{x,y,z,t\}$. It is shown that the $G'/G$-expansion method with the help of symbolic computation may provide us with a straightforward, effective and alternative mathematical tool for solving nonlinear evolution equations in mathematical physics. 2010 Mathematics Subject Classification: 35Q99, 83C15 Full text: PDF