A heuristic guide to nonlinear dispersive wave equations and soliton-type solutions

In this paper we present a heuristic way of constructing nonlinear dispersive equations that lead to soliton or soliton-type solutions. We assume only that a general knowledge of the dispersion relation of the system is known, together with some insight into the effect of nonlinearity on wave speed. We show that such knowledge is sufficient to derive most known soliton equations and thus to provide the engineer with a quick way to assess whether or not his particular system is likely to exhibit soliton behavior. Naturally, a more detailed description requires knowledge of the basic equations governing the system and special techniques to handle initial conditions. To that purpose we provide the reader with ample references which he may want to consult in order to augment the information gained by the method outlined in this paper.