Analysis methods for structures of dissipative and nondissipative jumps in dispersive systems

The interrelation between the theories of dissipative and nondissipative jumps is elucidated. Various methods are discussed for finding jump structures in dissipative, weakly dissipative, and nondissipative media with dispersion: relaxation, averaged equations, and a search for a jump structure by solving a set of ordinary differential equations with the use of projection. Previously published methods designed for nondissipative jumps are further elaborated. It is shown that nondissipative jump structures can be used as internal jump structures in weakly dissipative media, and, on the contrary, after introducing weak dissipation into the equations, nondissipative structures can be analyzed by the relaxation technique. Methods for finding jump structures that apply to both dissipative and nondissipative cases are described, and their efficiency is compared.