Nonlocal residual symmetries, N-th Bäcklund transformations and exact interaction solutions for a generalized Broer–Kaup–Kupershmidt system

The nonlocal residual symmetries of a generalized Broer–Kaup–Kupershmidt system are constructed using the truncated Painlevé expansion. By considering appropriate potential variables, these nonlocal symmetries are localized into Lie point symmetries by prolonging the generalized Broer–Kaup–Kupershmidt system to an enlarged system. Moreover, multiple residual symmetries of the studied system are derived, their localization is performed, and the N-th Bäcklund transformation theorem is presented. Furthermore, some exact interaction solutions between solitons and various kinds of nonlinear waves are formulated in view of the new consistent tanh expansion method.