Non-local residual symmetry and soliton-cnoidal periodic wave interaction solutions of the KdV6 equation

Abstract

The residual symmetry of the KdV6 equation is obtained by the Painlevé truncate expansion. Since the residual symmetry is non-local, five field quantities are introduced to localize it into the local one. Besides, the interaction solutions between solitons and cnoidal periodic waves of the KdV6 equation are constructed by making use of the consistent tanh expansion method. As an illustration, a specific interaction solution in the form of tanh function and Jacobian elliptic function is discussed both analytically and graphically.