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The consistent tanh expansion (CTE) method is applied to the cubic generalised Kadomtsev–Petviashvili (CGKP) equation. The interaction solutions between one kink soliton and the cnoidal periodic waves are explicitly given. Some special concrete interaction solutions in terms of the Jacobi elliptic functions and the third type of incomplete elliptic integral are discussed both in analytical and graphical ways.

Interaction Behaviours Between Soliton and Cnoidal Periodic Waves for the Cubic Generalised Kadomtsev–Petviashvili Equation