By the complete discrimination system for the polynomial, we give the classification of single travelling wave solutions to the Camassa–Holm–Degasperis–Procesi equation for some values of the convective parameter.

A wide range of two-dimensional nonlinear wave is described by Kadomtsev–Petviashvili (KP) equation. We obtained the classification of travelling wave patterns to the generalised KP equation with high-ordernonlinear dispersive and dissipative terms. Among these patterns, some new phenomena can be acquired for the first time. Representations of wave propagation patterns were achieved by taking specific values of parameters. This means that all these patterns can be realised under appropriate physical conditions.