Residual Symmetries and Interaction Solutions for the Classical Korteweg-de Vries Equation

The non-local residual symmetry for the classical Korteweg-de Vries equation is derived by the truncated Painleve analysis. This symmetry is first localised to the Lie point symmetry by introducing the auxiliary dependent variables. By using Lie's first theorem, we then obtain the finite transformation for the localised residual symmetry. Based on the consistent tanh expansion method, some exact interaction solutions among different non-linear excitations are explicitly presented finally. Some special interaction solutions are investigated both in analytical and graphical ways at the same time.