Whitham modulation theory is a nonlinear wave modulation theory [1] that can be used to study dispersive shock waves (see photograph above). The main idea is to separate the scales into a periodic traveling wave and its slow modulation. Writing evolution equations for solution parameters one can study stability properties of traveling wave solutions, including computations of growth rates and collisions of non-solitonic initial conditions. This approach does not rely on integrability of the equation, and thus has a broad range of applicability.

[1]: G.B. Whitham, Non-linear dispersive waves, Proc. R. Soc. Lond. Ser. A 283 238–261, 1965.