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This note shows that in looking for exact solutions to nonlinear PDEs, thedirect method of functional separation of variables can, in certain cases, bemore effective than the method of differential constraints based on thecompatibility analysis of PDEs with a single constraint (invariant surfacecondition). This fact is illustrated by examples of nonlinearreaction-diffusion and convection-diffusion equations with variablecoefficients, nonlinear Klein--Gordon type equations, and hydrodynamic boundarylayer equations. A few new exact solutions are given.

The direct method of functional separation of variables can provide more  exact solutions than the compatibility analysis of PDEs based on a single  differential constraint