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.