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 $n$th 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.

中文翻译：

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广义色散水波系统的非局部残差对称性和精确的相互作用解

为广义色散水波（GDWW）系统构造了非局部残差对称性。线性叠加的多个残差对称性被呈现和局部化，从而导致$ñ$行列式的Bäcklund变换。基于截断的Painlevé展开和一致的tanh展开（CTE）方法之间的直接联系，我们得出了精确的相互作用解，它们描述了孤子与共振孤波，误差函数波，周期波和有理函数波的相互作用。