Hyperbolic, trigonometric, and rational function solutions of Hirota-Ramani equation via \((G'/G)\)-expansion method (Q410382)

Summary: The \((G'/G)\)-expansion method is proposed to construct the exact traveling solutions to Hirota-Ramani equation: \(u_t - u_{xxt} + au_x (1 - u_t) = 0\), where \(a \neq 0\). Our work is motivated by the fact that the \((G'/G)\)-expansion method provides not only more general forms of solutions but also periodic and solitary waves. If we set the parameters in the obtained wider set of solutions as special values, then some previously known solutions can be recovered. The method appears to be easier and faster by means of a symbolic computation system.