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

By A. Salas, S. CesarA.Gómez. 2010

107 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/cce95ac337ec3c232b276d00526375d9d50a1143

Citations in the corpus

• The modified benjamin-bona-mahony equation via the extended generalized riccati equation mapping method (2012, unknown): “The investigation of traveling wave solutions of the nonlinear partial differential equations (PDEs) plays the most important role in the study of nonlinear physical phenomena which arise in mathematical physics, engineering sciences and other technical arena [1-43].”