Application of the Cole‐Hopf Transformation for Finding Exact Solutions to Several Forms of the Seventh‐Order KdV Equation

We use a generalized Cole‐Hopf transformation to obtain a condition that allows us to find exact solutions for several forms of the general seventh‐order KdV equation (KdV7). A remarkable fact is that this condition is satisfied by three well‐known particular cases of the KdV7. We also show some solutions in these cases. In the particular case of the seventh‐order Kaup‐Kupershmidt KdV equation we obtain other solutions by some ansatzes different from the Cole‐Hopf transformation.