Weak Transversality and Partially Invariant Solutions
  New exact solutions are obtained for several nonlinear physical equations, namely the Navier-Stokes and Euler systems, an isentropic compressible fluid system and a vector nonlinear Schroedinger equation. The solution methods make use of the symmetry group of the system in situations when the standard Lie method of symmetry reduction is not applicable. 
A. M. Grundland, P. Tempesta and P. Winternitz