The \(\varvec{(2+1)}\)-dimensional Konopelchenko–Dubrovsky equation: nonlocal symmetries and interaction solutions

The nonlocal symmetries for the \((2+1)\)-dimensional Konopelchenko–Dubrovsky equation are obtained with the truncated Painleve method and the Mobious (conformal) invariant form. The nonlocal symmetries are localized to the Lie point symmetries by introducing auxiliary dependent variables. The finite symmetry transformations are obtained by solving the initial value problem of the prolonged systems. The multi-solitary wave solution is presented with the finite symmetry transformations of a trivial solution. In the meanwhile, symmetry reductions in the enlarged systems are studied by the Lie point symmetry approach. Many explicit interaction solutions between solitons and cnoidal periodic waves are discussed both in analytical and in graphical ways.