Travelling wave solutions to a higher order KdV equation.

*(English)*Zbl 0732.76012Summary: This paper presents a direct method for the construction of travelling wave solutions to a higher order KdV equation. The method is based on a general form of solution to both the KdV equation and the fifth order KdV equation. In this approach a number of unknown constants are involved, and it is shown that the equations governing them are properly determined. The form of the solution depends on the signs of the coefficients b and c in the higher order KdV equation.

##### MSC:

76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |

35Q53 | KdV equations (Korteweg-de Vries equations) |

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\textit{A. Jeffrey} and \textit{M. N. B. Mohamad}, Chaos Solitons Fractals 1, No. 2, 187--194 (1991; Zbl 0732.76012)

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