Extended rotation and scaling groups for nonlinear diffusion equations (Q939422)

The essence of the paper is to consider solutions of various forms of the \((1+1)\)-dimensional nonlinear diffusion equation by means of the criterion of invariance under the action of some particular group. In each case a single differential equation containing several unknown functions is obtained. This is clained to be impossible to be solved and so various multitudinous special cases are presented in which it is possible to obtain a solution. Curiously the solutions tend to be quite simple and one wonders how the authors were able to concoct the often complex Ansätze to reach these solutions.