  We investigate the integrability of Nonlinear Partial Differential Equations
(NPDEs). The concepts are developed by firstly discussing the integrability of
the KdV equation. We proceed by generalizing the ideas introduced for the KdV
equation to other NPDEs. The method is based upon a linearization principle
which can be applied on nonlinearities which have a polynomial form. We
illustrate the potential of the method by finding solutions of the (coupled)
nonlinear Schr\"{o}dinger equation and the Manakov equation which play an
important role in optical fiber communication. Finally, it is shown that the
method can also be generalized to higher-dimensions.
