Classification of Optimal Group-Invariant Solutions: Cylindrical Korteweg‐de Vries Equation

Classification of optimal group‐invariant solutions has been carried out for cylindrical Korteweg–de Vries equation. It is a nonlinear evolution equation often found in studies of fluid mechanics and plasmas. An optimal system of subalgebras is obtained for the group of Lie generators associated with the equation, and then, the group‐invariant solutions are obtained for each member in the optimal class. The procedure for calculating other group‐invariant solutions from the optimal class is also illustrated with an example.