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Application of the Cole-Hopf transformation for finding exact solutions to several forms of the seventh-order KdV equation. (English) Zbl 1191.35236
Summary: 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.
MSC:
35Q53KdV-like (Korteweg-de Vries) equations