A study on the bilinear Caudrey–Dodd–Gibbon equation

In this paper we consider the Hirota transformation of the Caudrey–Dodd–Gibbon equation (CDGE) from another point of view. As a result, the local equivalence between the CDGE and its bilinear equation is established, and a new type of Bäcklund transformation, which is defined by a second-order ODE along with the appropriate initial values, is presented to construct new solutions for the bilinear CDGE from the seed solutions of original CDGE.