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

Alvaro H. Salas and Cesar A. Gómez S.

Mathematical Problems in Engineering, 2010, vol. 2010, 1-14

Abstract:

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.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:194329

DOI: 10.1155/2010/194329

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