The foundations of nonlinear optics are revisited, and the formalism is applied to waveguide modes. The effect of loss and dispersion are included rigorously along with the vectorial nature of the modes, and a new version of the nonlinear Schrödinger (NLS) equation is derived. This leads to more general expressions for the group index, for the group-index dispersion (GVD), and for the Kerr coefficient. These quantities are essential for the design of waveguides suitable for e.g. the generation of optical frequency combs and all-optical switches. Examples are given using the silicon nitride material platform. Specifically, values are extracted for the coefficients of the chi-3 tensor based on measurements of Kerr coefficients and mode simulations.