Extended rotation and scaling groups for nonlinear evolution equations (Q5917471)

The \((l+1)\)-dimensional \(k\)th-order nonlinear evolution equation \(u_t=E(x,u,u_1,\cdots,u_k)\) is considered, where \(u_i\) is the \(i\)th partial derivative with respect to the space variable \(x\) and \(E\) is a smooth function of its variables. The authors introduce nonlinear extensions of the rotation group in \(\mathbb{R}^2\) and the scaling group, both of them with corresponding invariant sets, on the base of which exact solutions of the evolution equation are constructed.