ABSTRACT
In real life, we will of course never encounter a wave phenomenon which can truly be called linear (with the exception of the classical description of electromagnetic waves in vacuum), although a description based on a linear formalism as in the foregoing section can be very good, in some cases even extremely good. To describe the lowest order nonlinear corrections to the basic linear wave analysis, it is an advantage to classify wave-types according to their dispersion relation. The important observation will be that many nonlinear wave phenomena can be “classiÀed” into either Korteweg-deVries types or nonlinear Schro¨dinger types, as explained in detail later. These two are the most relevant ones for plasma physics, but there are also others. The basic classiÀcation is rooted in the linear dispersion relation, where we here distinguish two cases.
