Bäcklund transformation and soliton–cnoidal wave interaction solution for the coupled Klein–Gordon equations

Abstract

In this paper, Backlund transformation and interaction solutions of the generalized coupled Klein–Gordon (cKG) equations with the variable coefficients are studied via the residual symmetry and the consistent Riccati expansion (CRE) method. From the truncated Painleve expansion, we drive the residual symmetry which can be transformed into the local Lie point symmetry. The multiple residual symmetries are established and nth Backlund transformation in terms of determinant is presented. The cKG equations are proved to be CRE solvable by using the CRE method. More importantly, we construct exact interaction solutions between soliton and cnoidal periodic wave. It is shown that when the modulus of the Jacobi elliptic function tends to one, the interaction solutions degenerate to the special resonant soliton solutions. Moreover, these reduced resonant soliton solutions exhibit the interesting properties which differ from the usual resonant soliton solutions.