Lie point symmetry preserving discretizations for variable coefficient Korteweg-de Vries equations (Q1577388)

The authors consider the variable coefficient Korteweg-de Vries equation, which describes the propagation of long waves in shallow water under general conditions. The variable coefficients are so chosen that the equation has a three-dimensional Lie point symmetry group. An invariant difference model (a difference equation and a mesh) is presented, preserving all the Lie point symmetries of the original equation. One of the benefit of this method is that group invariant solutions can be obtained for the discrete equation in the same way as for the continuous one.