Explicit soliton–cnoidal wave interaction solutions for the (2+1)-dimensional negative-order breaking soliton equation

By using the truncated Painlevé expansion, we construct the residual symmetry for the (2+1)-dimensional negative-order breaking soliton equation. It is found that such nonlocal symmetry can be transformed to local Lie point symmetries by introducing auxiliary variables. The multiple residual symmetries are presented via the linear superposition of the single one. Based on the localized multiple residual symmetries, the n-th Bäcklund transformation is obtained in terms of determinant. Via the aid of the link between the truncated Painlevé expansion and the CTE method, we derive the explicit soliton–cnoidal wave interaction solutions for the (2+1)-dimensional NBS equation.