The reductive perturbation methods for the wave propagation in weakly inhomogeneous media and also spatially homogeneous but weakly unstable media are developed in virtue of appropriate strained variables for the waves and the media. For each case, low dispersive long wave and modulated amplitude of the self-interacting nearly monochromatic wave can be described by relatively simple scalar equations, many of which have one linear extra term with a variable coefficient in comparison with the equation for the constant media. Modulation of nearly monochromatic wave which has a complex frequency with a small imaginary part, is also considered in an unsteady medium and a similar governing equation is obtained. These theories are applied, directly or in extended forms, to the illustrative examples from fluid mechanics, plasma physics and astrophysics.