First, by improving some key steps in the homogeneous balance method, a new auto-Bäcklund transformation (BT) to the KdV equation with general variable coefficients is derived. The new auto-BT in this paper does not require the coefficients of the equation to be linearly dependent. Then, based on the new auto-BT in which there is only one quadratic homogeneity equation to be solved, an exact soliton-like solution containing 2-solitary wave is given.
"A New Auto-Bäcklund Transformation of the KdV Equation with General Variable Coefficients and Its Application." Abstr. Appl. Anal. 2014 1 - 5, 2014. https://doi.org/10.1155/2014/591982