Nonlocal residual symmetries and exact interaction solutions for the generalized dispersive water waves system

Nonlocal residual symmetries are constructed for the generalized dispersive water waves (GDWW) system. The linear superposed multiple residual symmetries are presented and localized, which give rise to nth Bäcklund transformation in terms of determinant. Based on the direct connection between the truncated Painlevé expansion and the consistent tanh expansion (CTE) method, we derive exact interaction solutions which describe soliton interacting with resonant soliton wave, error function wave, periodic wave and rational function wave.