Abundant interaction solutions of the integrable (1 + 1)‐dimensional coupled KdV system

Abstract

Based on the Hirota bilinear method and the consistent tanh expansion method, we study different interaction excitations of the integrable ‐dimensional coupled KdV system, which is a typical and essential water wave model in the two‐layer fluid. Abundant new interaction solutions including lumps, lump–kink solution, breathers, two‐kink solution, resonant soliton, and soliton–cnoidal solution are obtained. All these exact solutions are shown both analytically and graphically with proper constant selection.