A coupled KdV system: Consistent tanh expansion, soliton-cnoidal wave solutions and nonlocal symmetries

In this paper, a coupled KdV system is shown to be solvable, having a consistent tanh expansion solution. From the consistent tanh expansion solution, a kind of soliton-cnoidal interaction solution is obtained explicitly. Moreover, the nonlocal symmetries related to the truncated Painlevé expansion and the corresponding transformation groups are also given.