Some new exact solutions for a generalized variable coeffi- cients KdV equation

In this paper, the variable coefficients KdV equation with general power nonlinearities is proposed. Firstly, it is transformed into a generalized KdV equation with constant coefficients using a point transformation. Then, the traveling wave transformation is utilized to transform the obtained constant coefficients generalized KdV equation into a generalized ordinary differential equation. We give a classification for the obtained generalized ordinary differential equation using a suitable integrating factor. Some new solutions are obtained for the generalized KdV equation with constant coefficients. All the obtained solutions in this paper for the variable coefficients KdV equation with general power nonlinearities are new.

Automated summary

In this paper, the variable coefficients KdV equation with general power nonlinearities is transformed into a generalized KdV equation with constant coefficients using a point transformation. Then, the traveling wave transformation is utilized to convert the equation into a generalized ordinary differential equation. A classification is given for the obtained equation using an integrating factor, and new solutions are obtained for the equation. All the solutions obtained in this paper are new.