Nonlinear dispersion relations

We examine how nonlinear dispersion relations (NLDR) can be used as a simple, universal algebraic tool to provide information for the localized, nonlinear solutions of PDE that model physical systems. Such scaling relations between width, amplitude and velocity are of great help for numerical investigations of nonlinear solutions. The methodology is applied to a variety of examples from diverse branches of physics, both Hamiltonian as well as dissipative ones. The limitations of the approach are also discussed.