Institute for Geophysics,

32 Palladin Ave.,

03680 Kyiv,

UKRAINE

and

University of Strathclyde,

Richmond St.,

Glasgow G1 1XH,

UK

E-mail: vakhnenko@bitp.kiev.ua, ejp@maths.strath.ac.uk

**The graphical interpretation of the solutions of a
generalized Degasperis-Procesi equation**

**Abstract:**

By generalizing the Degasperis-Procesi equation, we have suggested
a new evolution equation. It can be integrated in a similar way to the
Degasperis-Procesi equation in order to find travelling-wave solutions.
It turns out that the solutions of this new equation can be interpreted
as the projection of a spiral on a plane at different projection angles
to the axis of the spiral. The separated solutions appear when we consider
the spiral with the extended upper or/and lower parts. The solutions to
the Degasperis-Procesi and Camassa-Holm equations can be interpreted in
a similar way.